COMPARATIVE STUDY OF THE EXCITATION
SYSTEM, AVR AND PSS MODELS FOR
SYNCHRONOUS GENERATORS UNDER THE PHASE
TO GROUND FAULT
A THESIS SUBMITTED TO THE
GRADUATE SCHOOL OF APPLIED SCIENCES
OF
NEAR EAST UNIVERSITY
By
SALIH M. EL SHARIF ABDALLA
In Partial Fulfillment of the Requirements for the Degree of
Master of Science
In
Electrical and Electronic Engineering
NICOSIA, 2015
I hereby declare that all information in this document has been obtained and presented in
accordance with academic rules and ethical conduct. I also declare that, as required by these
rules and conduct, I have fully cited and referenced all material and results that are not
original to this work.
Name: SALIH M. EL SHARIF ABDALLA
Signature:
Date:
i
ACKNOWLEDGEMENTS
Firstly, I would like to thank God for giving me the fortitude to complete my thesis. I would
like to thank my supervisors Assoc. Prof. Dr. Özgür Cemel Özerdem for his constant
guidance, advice and support with the development of my work. Also I would like to
acknowledgement chairman Assist. Prof. Dr. Ali Serener and all the staff in the Electrical and
Electronic Engineering Department for their supports to me. Also, I would like to thank Near
East University for accepting me as a master student.
I would like to thank my mother for her love, support and patience every day. This thesis is
dedicated to you. Finally, and most importantly, the constant support of my wife, Fatten,
through the years has been the foundation, on which this thesis was built.
ii
ÖZET
Bu tezin temel hedefi geçici rejim durumunda senkron jeneratör tahrik sistemlerinin, otomatik
gerilim regulatörü (AVR) ve güç sistemleri stabilizörü (PSS) nğn davranışını incelemektir.
Öncelikle geçici rejim stabilitesi teorisiyle ilgili dönüşüm denklemleri, transfer reaktansı, güç
açısı grafiği ve kritik geçiş tamanı irdelenmiştir.
Tezde geçici rejim stabilitesi için çözüm dönüşüm eğrileri ve diferansiyel cebir denklemleri
metodları kullanılarak aranmıştır. POWER-WORLD yazilimi bu konunun incelenmesi için
kullanılmıştır. Çok üreteçli dokuz baralı bir sistem POWER-WORLD simulasyonu ile
irdelenmiştir. Bu durumda bir çok geçici rejim durumu irdelenmiştir ve hepsinde arıza
literatürde stabilite için gerekli olan 0.1 saniyede giderilmiştir. Tezin amacı olan AVR ve PSS
tahrik sistemleri irdelenmiş ve röle ayarları için gerekli çeşitli güç parametrelerinin
belirlenmesinde yardımcı olacak bir çalışma gerçekleştirilmiştir.
Anahtar kelimeler: Automatic Voltage Regulator (AVR), excitation systems, Power System
Stabilizer (PSS)
iii
ABSTRACT
In this thesis, the performance monitoring of synchronous generator excitation system,
automatic voltage regulator (AVR) and power system stabilizer (PSS) under
transient
stability is the main purpose. Initially, the theory concerning to transient-stability and the
transfer reactance, swing Equation, power angle curve and the critical clearing time has been
discussed.
In this thesis, possible methods of transient stability have been studied with the solution for
swing curve and differential-algebraic Equations method. The POWER-WORLD software is
used to study the transient stability issues by using this method.
A POWER-WORLD simulation has been carried out to testify the performance of the multimachine nine-bus system. For the method, the transient studies are tested in multi cases. For
all cases, the fault cleared at time t = 0.1 second. In study of previous researched, proved that
the system is stable at this period, The object of this research is to study performance of the
excitation system, AVR and PSS. The program is helpful in determining voltage limit of
systems and transfer energy between systems, critical power angle and critical clearing times
for circuit-breakers. So, a better relay setting can be proposed.
Keywords: Automatic Voltage Regulator (AVR), excitation systems, Power System
Stabilizer (PSS)
iv
With love to my wife and all my family who have been always with me . . .
v
TABLE OF CONTENTS
AKNOWLEDGMENTS …………………………………………...………………..…..
ii
ÖZET……………………………………………………………………………………..
iii
ABSTRACT…………………………………………………………………….……..…. iv
TABLE OF CONTENTS…………………………………………………...…………...
vi
LIST OF TABLES……………………………………………………………….…...….
viii
LIST OF FIGURES …………………………………………………………….....…….
ix
LIST OF USED SYMBOLS........……..……………………………..……………..…… xi
LIST OF USED ABBREVATIONS…………………………………………...….…….
xii
CHAPTER 1: INTRODUCTION
1.1 Introduction…...…………...…………..…...…………………………........................
1
1.2 Literature Review………...……...………………………………................……....…
2
1.3 Thesis Overview………...…………………………………………..........…….….….
4
CHAPTER 2: POWER SYSTEM STABILITY
2.1 The Stability Problem…...…………...…………..……………………….................... 5
2.1.1 Rotor Angle stability…...……….…...………….……...…………..….…...........
6
2.1.2 Frequency stability…...…………...………..….……..….....……..……..…........
6
2.1.3 Voltage Stability…...………..........………….……......…..…..………….….......
7
2.2 Effect of Power-Angle …………..…...…………...………..…………….................... 7
2.3 Swing Equations ...........................................................................................................
9
2.4 Multi-Machine Transient Stability…...…………...……….……...……......................
11
2.5 The Swing Equations For Multi Machine System …...……...……...……….….........
12
2.6 Phase To Ground Fault …...…………...…………..……...……………….....…........
13
2.7 Transient Stability…...…………...…………..……………...……………..……........
16
vi
CHAPTER 3: RESPONSE SYSTEMS
3.1 Response Systems…...………………..……..………………………...…….…..........
18
3.2 Generation Control Systems…...………………..…….………….….....…..…...........
18
3.2.1 Governing System …...……………..…………....…..........…...........................
19
3.2.2 Exciters…...…………....……..…….....…………………...……………..........
20
3.2.2.1 AC Exciters (Brushless) …....…………….…………..………….........
20
3.2.2.2 Static Exciters (Brushed) …....…………...……………..………..........
21
3.2.2.3 Over Excitation Limiter…...……….….…..…..…...….….………........
21
3.2.2.4 Under Excitation Limiter…...………….……..……….……….…........
21
3.2.3 Automatic voltage regulator AVR…...........………….…...…………….…......
22
3.2.3.1 Type AC1A…...….………...…………...…….……………...…...........
23
3.2.3.2 Type ST1A…...………..……...…..…………………………...….........
24
3.2.4 Power System Stabilizer PSS…...……..…...…..………….………..…............. 25
3.2.4.1 PSS1A Power System Stabilizer…..........…………………...…...........
26
3.2.4.2 PSS2A Power System Stabilizer…...………..….…………...…...........
26
CHAPTER 4: RESULTS AND DISCUSSIONS
4.1 Power System Simulation And Models……...…………….........................................
29
4.2 The Effect Of Fault Location And Fault Clearing Time ………………..…….…….. 30
4.3 The Comparative Method ………………………...…………...…..…………………
31
4.4 Power-World ……………………………………………………..…….…...……….. 31
CHAPTER 5: CONCLUSION
5.1 Conclusion………………...…...……………………...……………...……....……….
51
REFERENCES..........................………………………………………...……...…..……. 53
APPENDIX A: Reduced And Generator Data…………………………………...………
57
APPENDIX B: Excitation System, AVR And PSS Models……………………………... 58
APPENDIX C: Before Fault And Fault Analysis…………………………………….…
62
APPENDIX D: Transient Analysis……………………………………………....………
65
APPENDIX E: Differential- Algebraic Equations Method ………………….…….……. 71
vii
LIST OF TABLES
Table. 4.1: Excitation system models, AVR and PSS……….….…….…….…………...
viii
31
LIST OF FIGURES
Figure 2.1: One System……………………………………..………...........…………….
8
Figure 2.2: The Power-Angle Curve …………………………….………………....….... 9
Figure 2.3: Single-Line-To-Ground Fault…………………………..………...……....….
14
Figure 2.4: Single Phase Fault………………………….……..……………..…...…...….
14
Figure 2.5: Thevenin Equivalent Of The Sequence Network……………………...….…. 15
Figure 3.1: The system structure………………..…………………….....................…….
18
Figure 3.2: Functional block diagram of hydraulic turbine governing system. ……....…. 19
Figure 3.3: A.C. Exciter…………………..………………………..…………………...... 20
Figure 3.4: Static Exciter……………………..……………………….…………........….
21
Figure 3.5: The block diagram of the AVR………………..……………………….....….
22
Figure 3.6: Type PSS1A power system stabilizer model……………………………..….
23
Figure 3.7: Type PSS2B power system stabilizer model……………………….….....….
24
Figure 3.8: Type AC1A excitation system model……………………………...…….…..
26
Figure 3.9: Type ST1A excitation system model………………………...…...……....….
28
Figure 4.1: Multi-machine, 9-bus system…………………………....………...….….…..
30
Figure 4.2: Multi-machine, 9-bus system before-fault With power-world……....…...….
32
Figure 4.3: Rotor angle before fault…….…………………………………….…........….
32
Figure 4.4: Speed before fault………………….………………...…………...............….
33
Figure 4.5: Excitation before fault…………………………...….…….………….......….. 33
Figure 4.6: Multi-machine, 9-bus system during-fault With power-world……….......….
33
Figure 4.7: Multi-machine, 9-bus system after-fault With power-world….…..................
34
Figure 4.8: Case 1-ST1A with PSS1A………….………………..……………….......….
35
Figure 4.9: Case 1-ST1A with PSS1A…………………………..…………...............….
36
Figure 4.10: Case 1-ST1A with PSS1A………………………………….....……...…….
36
Figure 4.11: Case 1-ST1A with PSS1A………………….…………………...….......….
36
Figure 4.12: Case 2-ST1A without - PSS……………………………….….........…..….
37
Figure 4.13: Case 2-ST1A without - PSS……………………………….…......…......…. 38
Figure 4.14: Case 2-ST1A without - PSS……………………………….……..…......…. 38
ix
Figure 4.15: Case 2-ST1A without - PSS……………………………….…......……....... 38
Figure 4.16: Case 3-ST1A with PSS2A………………………..………......….……...…. 39
Figure 4.17: Case 3-ST1A with PSS2A………………………..…………..…....…...….
40
Figure 4.18: Case 3-ST1A with PSS2A………………………….………….……….….
40
Figure 4.19: Case 3-ST1A with PSS2A……………………………………….…...…....
40
Figure 4.20: Case 4-AC1A with PSS1A………………………………………..........….
41
Figure 4.21: Case 4-AC1A with PSS1A………………………………………..........….
42
Figure 4.22: Case 4-AC1A with PSS1A………………………………................…..….
42
Figure 4.23: Case 4-AC1A with PSS1A…………………………………...…….......….
42
Figure 4.24: Case 5-AC1A without - PSS……………………………..………...…...….
43
Figure 4.25: Case 5-AC1A without - PSS……………………………..………...…...….
44
Figure 4.26: Case 5-AC1A without - PSS……………………………...……....…….….
44
Figure 4.27: Case 5-AC1A without - PSS……………………………...…….....…....….
44
Figure 4.28: Case 6-AC1A with - PSS2A……………………………………...…….….
45
Figure 4.29: Case 6-AC1A with - PSS2A………………………………………...….….
46
Figure 4.30: Case 6-AC1A with - PSS2A…………………………..…………...…...….
46
Figure 4.31: Case 6-AC1A with - PSS2A……………………………………......…..….
46
Figure 4.32: Acceleration- ST1A without PSS……..………………….……..............….
47
Figure 4.33: Acceleration- ST1A with PSSA1……………….…………..……..……….
47
Figure 4.34: Acceleration- ST1A with PSS2A……………………………..…..…....…..
47
Figure 4.35: Acceleration- AC1A without PSS……………..……………..…..……...…
48
Figure 4.36: Acceleration - AC1A with PSS1A………………………….…...………….
48
Figure 4.37: Acceleration- AC1A with PSS2A………………………………….........…. 48
Figure 4.38: AC1A without - PSS is unstable with time 0.3s………………...…......…...
49
Figure 4.39: AC1A without - PSS is unstable with time 0.3s…….………...……......…..
49
Figure 4.40: AC1A without - PSS is unstable with time 0.3s…….……….……..............
50
Figure 4.41: ST1A without - PSS is stable with time 0.3s………..…………..….............
50
Figure 4.42: ST1A without - PSS is stable with time 0.3s……………….….........……...
50
x
LIST OF USED SYMBOLS
:
:
r :
s :
D:
Ef :
Efd :
ER :
G(s), G(t) :
GEP(s) :
H:
If :
J:
KA :
Mm Mc :
P:
Pa :
Pe :
PID :
Pm :
Pmax :
Q:
Ta
TA,TE,KE,SE:
Td’ :
Td’’ :
Td0’ :
Td0’’ :
Te :
Tm :
Tq’’ :
Tq0’’ :
Vf :
VREF :
Vs :
Xd, Xq :
Xd’, Xq’ :
The angular position of the rotor in rad.
The angular position in rad.
Angular speed of the rotor.
Synchronous speed in rad/s.
Damping coefficient (pu)
Field voltage V.
Output field voltage from field-generator V.
Output voltage of the voltage regulator amplifier.
The low-pass filter transfer function.
Transfer function of the stabilizer output.
Inertia constant.
Field current A.
The total moment of inertia of the rotor mass in kgm2.
Gain of the voltage regulator amplifier.
Mechanical torque and electromagnetic torque.
Active power MW.
Accelerating power in MW.
Electrical power MW
Proportional integral derivative.
Mechanical power MW.
V1V2/X is the maximum power can be transmitted over the line.
Reactive power MVAR.
Accelerating torque.
Parameters of The exciter.
The d-axis transient short-circuit time constant s.
The d-axis subtransient short-circuit time constant s.
The d-axis transient open-loop time constant s.
The d-axis subtransient open-loop time constant s.
The electrical torque output of the alternator in N-m.
The mechanical torque supplied by the prime mover in N-m.
The q-axis subtransient short-circuit time constant s.
The q-axis subtransient open-loop time constant s.
Voltage at the faulted.
Reference voltage, voltage regulator V.
PSS voltage.
The d-,q-axis synchronous reactance (pu)
The d-,q-axis transient reactance (pu)
xi
LIST OF USED ABBREVIATIONS
AVR :
Automatic voltage regulator.
BE :
Brushless exciter.
CCT :
The critical clearing time.
EX :
Excitation systems.
FCL :
Field current limiting.
FCT :
Fault clearing time.
IEEE :
Institute of Electrical and Electronic Engineers.
MX :
Main exciter.
OEL :
Over excitation limiter.
PSS :
Power system stabilizer.
PU :
Per unit.
SC :
Short circuit.
SG :
Synchronous generator.
UEL :
Under excitation limiter.
xi
xii
CHAPTER 1
INTRODUCTION
1.1 Introduction
In this study, power system stabilizer (PSS) and automatic voltage regulator (AVR) were
studied to ameliorate the transient stability of generator in power system. The design
problem of AVR and PSS were studied, and their performances were tested.
The complex torque coefficient is observed by the time domain simulation. The test signal
method is chosen for this purpose. The studied system consists of a multi-machine with
slack bus system. Two types of excitation systems, AVR IEEE AC1A, ST1A excitation
systems, and two types of PSS1A Power System Stabilizer, PSS2A Power System
Stabilizer are chosen. The
impacts of excitation systems with high response on the
electrical damping are inspected. Six cases, the excitation system without PSS and with
PSS are considered. At the same time, different input signals of PSS are used. The impacts
of the parameters of PSS on the electrical damping are also studied.
The transient stability (large signal) stability problems have been studied such as phase to
ground fault in power systems and which produced studies in many literatures power
system is influenced by high electromechanical oscillations while a disturbance happens,
which may cause to loss of synchronism of generators. High performance excitation
systems are substantial to keep steady state and transient stability of generators and provide
fast control and supported of terminal voltage. The generator excitation system using an
AVR keeps the terminal voltage magnitude of a synchronous generator to a acceptable
level. Also the excitation system and AVR provide to control the reactive power (Q) and
get better stability. The AVR assists improving the steady-state stability of power systems.
In transient state, machine is affected by disturbed impacts, especially in a short time that
causes clear drop on the terminal voltage of machine.
The controller to raise damping of electromechanical oscillations is well-known as PSS.
They are used to compensate the negative damping of AVR. Likewise, PSS is controlled
the input signal of excitation system to damp out rotor oscillations.
1
1.2 Literature Review
Transient stability analysis issues have been widely discussed in the literature. Many parts
of the stability problem have been covered with a lot of researches. Some of the
researchers have covered the analytical study of the power stability problems. Others have
focused on the methods of treatment and their effects on the stability. The discussion
focuses on issues such as rotor angle stability, frequency stability and voltage stability.
Other researches were
looking for if the system is stable or unstable with a large
disturbance such as a fault occurring (Wvong, 1989). In other researches, focus on a new
robust control methodology to improve the power system transient stability. While others
discussed the structure and comparison between performance of different devices to
improve the stability.
Many programs of stability analysis use simple step by step integration methods to solve
power system stability. While these methods have been applied for a long time, they can
still be used to types of models. They are well known and accepted by the system
operators. This allows easy analysis of the simulation in practice was discussed in
(Grainger and Stevenson, 1994).
The voltage of the power system generator could be very low during a large disturbance
such as a fault occurring on the generator bus, or in transmission lines near the generator,
was reported by (Anderson and Fouad, 1997). During the fault, the flow of the electrical
power to the power system is interrupted, and the generator rotor speed is risen by the
input mechanical power. After the protection circuit breaker has cleared the fault, the
generator is re-healthy to the power system and recapture the power supply to the system.
Usually, the results of post-fault oscillations caused by the energy stored in the generator
rotor during the cycles of the fault. The damper windings on the generator rotors can be
used to control the oscillation, but this style is very costly. Compared with damper
windings, the generator excitation control provides a better effective in cost and control.
The idea simply that the generator excitation control that regulates the terminal voltage of
the generator based on the terminal voltage feedback by the AVR. The AVR simply
increases the field voltage to quickly recover the terminal voltage to the normal situation
level. Such a quick recovery of the generator terminal voltage will force a negative effect
on the damping of the post-fault oscillation. The power system stabilizer (PSS) as a extra
controller to the AVR and generator excitation control, was reported in (Liu et al., 2007),
if suitable designed, could remove any negative effects on the damping of the post-fault
2
oscillation. Also was discussed and reported in (Kundur,,1994). Effect of a maximum
value of over excitation limiter during the fault, possible provided to the system, was
discussed in (Mummert, 1999).
In (Yeu, 2010) the small signal analysis of power systems are investigated by the power
control system is such as excitation system, AVR, PSS and governing system. In (Loen,
2014) many block was discussed. The mathematical models for excitation system
automatic voltage regulator (AVR), power system stabilizer (PSS). And study Performance
analysis of various control devices. In (Saadat, 1999), the different methods to study the
power flow solution steps of the stability systems studies.
In (Sumina et al., 2011) the power system stabilizer (PSS) is used in synchronous generator
excitation control system for damping electromechanical oscillations. The goal of the PSS
is to generate a stabilizing signal. And also the effects of different types of excitation
systems and PSS was studied in (Zhang and Xu, 2007). The output of the main exciter is a
nonlinear function of the inputs and which are related through the constant parameter, was
discussed in (Bhaskar et al., 2000). The most practical obtainable method of transient
stability analysis is time-domain simulation with the nonlinear differential Equations. In
(Bose, 1984), the critical clearing time is the limit time for which a power system is
allowed to stay in fault condition without losing stability. The accuracy and reliability of
power system by limiting impacts of faults on the power system that the breaker clearing
times should be corresponded with the normal critical clearing times. Suitable CCT
settings of covering the power system determine the reliability and stability of power
supply. Many papers have been discussed the transient stability analysis program used the
method integration method has been presented in (Gafari, 2013). Numerical simulation of
stochastic differential algebraic Equations for power system transient stability was
discussed in (Wang and Crow, 2011).
Some others papers and researches have been written and discussed in the field of transient
stability analysis. The subject of the power stability is a wide and very important.
3
1.3 Thesis Overview
The following is an outline of this thesis.
Chapter 1: Introduction to models of power systems, and a literature review discusses
published information in a transient stability analysis.
Chapter 2: Review of the issues, the stability problem, and rotor angle stability, frequency
stability and voltage stability of power system, the single phase earth fault in high
voltage distribution networks that are low impedance ground.
Chapter 3: Review of the issues, the need for generator excitation control, the automatic
voltage regulator AVR with or without power system stabilizer PSS, the design modern
control excitation in power system. This chapter presents the excitation system, and turbine
governor system for the design of an excitation control in this thesis.
Chapter 4: Simulations and results of the study for system analysis under single phase
fault using analysis simulation with power-world version 18 simulation.
Chapter 5: The conclusion of this thesis.
4
CHAPTER 2
POWER SYSTEM STABILITY
2.1 The Stability Problem
The stability problem was discussed, the power-angle relationship, swing Equation are
preface to our study. Then, the different parameters for which the analysis is offered
include the fault clearing time (FCT), damping coefficient, generator armature resistance
and fault location.
The single phase fault is mostly seen in networks, for this reason, in this thesis the single
phase earth fault in high voltage transmission lines that are low impedance grounded is
used. First, the basic of low impedance grounded system are discussed. The clearing time
of earth faults, and the fault location are discussed and effect were observed.
The stable of power system means that all its multi-generators are operating in
synchronism with the grid and with each other. The problems occur when the generators is
oscillated by disturbances that occur by transmission faults. There are two types of stability
problem in power systems. Firstly, the steady-state stability problem which mention to the
stability of power systems when a small disturbance happens in the power systems such as
a change in demands, manual or automatic changes in excitation system (Kundur, 1994).
Clearly, these small disturbances cannot cause loss of synchronism unless the system is
operating at procedure action, its steady state stability limit (Kundur, 1994). This limit is
the greatest power that could be transmitted in operating conditions in the steady state,
without loss of synchronism. The analysis of steady state stability need to referenced at
considerations of the solution of power flow Equations and swing Equations over a time
of a few minutes. Exciters and governor should also be included in the steady state stability
analysis (Saadat, 1999). Secondly, the transient stability problem that is occurred by a
large disturbance in the power system such as an unexpected loss of generators or loads,
circuit breaker close-open operations under large loads, or faults with circuit isolation.
Such large disturbances make a power without equilibrium between generation and loads
in the network. This unbalance appear at the generator shafts and causes the rotors to
oscillate until a new stability operating point is appeared, or until the rotors continue to
5
oscillate and deviate from each other and in the end some generators will lose
synchronism.
Loss of synchronism should be stopped or controlled because it has a troubling effect on
voltages, frequency and power, and it may cause dangerous damage to generators, which
are the most costly factors in power systems (Grainger and Stevenson,,1994). The
generators which tend to lose synchronism should be tripped and get out from the system
before any harm occurs, and then comeback to synchronism. In this case, can be done
easily with gas and water turbine generators, steam turbine generators need many long time
to rebuild steam and in this case, the operator has to shed loads to compensate for the loss
of generators, was discussed in (Anderson and Fouad,,1997). Loss of synchronism may
also cause some protection relays to trip the circuit breakers of lines. The problem becomes
very difficult and may result in more generators pulling out of synchronism.
2.1.1 Rotor Angle Stability
The rotor angle stability is known as the ability of multi- synchronous machines to keep in
synchronism under normal operating conditions and after being attacked by a disturbance.
Practically, the total active electrical power is given by the generators should be equal to
the active power (p) used by the demands, this contains also the losses in the network. This
equilibrium between the demand and generation can be correlating to the balance between
the generator input, or mechanical torque, and the generator output, or electrical torque. A
disturbance via system can annoyed this balance, that results in the acceleration or
deceleration of the rotors of the generators. If one of generators suddenly runs faster than
another, the angular position of its rotor close to that of the slower unit will increase. The
outcome angular difference transfers a some of the load from the slow generator to the fast
generator, depending on the power angle relationship, we will discuss next. This resort to
reduce the speed difference and the angular deviation. Any more increase in angular
deviation results in a decrease in power transfer, which can cause to instability (Agatep,
2013).
2.1.2 Frequency Stability
Frequency stability known as the ability of a power system to protect steady frequency. It
depends on the ability to keep or carry back balance between power system generation and
6
demand, with minimum loss of load. A idealistic cause for frequency instability is the loss
of generation causing the all system frequency to drop. The frequency stability problems
are connected with insufficiency in devices responses, harmony of control and protection
devices, or generation control devices.
2.1.3 Voltage Stability
Voltage stability is a part of general power system stability. It denote to the ability of a
power system to keep steady voltages at all bus bars in the system after being attacked by a
disturbance. The voltage stability according to (Padiyar,,2008), a power system with
operating point is small disturbance voltage stable if, after a small disturbance, voltages
near demands are comparable to pre disturbance values. A power system at a given
operating point and matter to a given disturbance is voltage stable if voltages near loads
draw near post disturbance balance values. voltage collapse if post-disturbance balance
voltages are below acceptable levels. Voltage collapse may be system large or ordinary.
The major factor causing to voltage instability is usually the voltage drop that occurs when
active and reactive power flow via inductive reactance’s connected with the transmission
line grid, as the line currents during different power flow conditions increase, the reactive
losses raise. When reactive losses raise, the voltage magnitude decreases. And, as the
active power flow increases the voltage magnitudes going to decrease. The system can no
longer backup the active power flow on the lines and keep a stable voltage. So, the voltage
collapses.
2.2 Effect of Power-Angle
In this thesis, the power-angle relationship are discussed. we will suppose this relationship
for a parameter as one body. Principally, consider the one-machine infinite bus bar system
shown in Figure 2.1. The reactance of system (x) is the total of the reactance of the
synchronous reactance (Xd, Xq) or the transient reactance of the generator (Xd’, Xq’) and
the power transmission line.
7
Figure 2.1: One system.
VS  V1 , VR  V2 0
IS 
(2.1)
V1  V2 V1 cos   V2  jV1 sin 

jX
jX
(2.2)
The active power and reactive powers are given as
PS  jQS  VS I S  V1 cos   j sin  
V1 cos   V2  jV1 sin 
 jX
(2.2)
It will be

V1V2 sin   j V12  V1V2 cos 
PS  jQS 
X

(2.3)
The total active power loss in line is very few, so the active power from the send-side is
equal to the active power at the receive-side.
Pe  PS  PR 
V1V2
sin   Pmax sin 
X
(2.4)
The power angle curve in Figure. 2.2. is shows that the input power( P0). There are two
values of the angle  , (0 and max). The angles are:
 P0
 Pmax
 0  sin 1 



(2.5)
 max  180   0
8
Figure 2.2: The power-angle curve
2.3 Swing Equation
The synchronous generator is driven by a turbine. Therefore, the Equation motion of the
machine rotor is given by
J
d 2
 Tm  Te  Ta
dt 2
(2.6)
When the losses are ignored, the difference between the electrical and mechanical torque is
known as accelerating torque (Ta). In the steady state, the electrical torque is equal to the
mechanical torque, for this reason, the accelerating power will be zero. During this time,
the rotor will shift at synchronous speed s according to (Saadat, 1999).
The angular position  belongs to a stationary reference scope. To represent it with respect
to the synchronously rotating scope, it becomes:
  st  
(2.7)
The time derivative of the last Equation, is:
d
d
 s 
dt
dt
(2.8)
9
The angular speed of the rotor as:
r 
d
dt
We can re-write (2.8) as
r  s 
d
dt
(2.9)
The rotor angular speed is equal to the synchronous speed only when ddt is equal to zero.
where ddt is the error in speed. The derivative of (2.8), we can re-write as
J
d 2
 Tm  Te  Ta
dt 2
(2.10)
Multiplying both side of (2.10) by m
d 2
 Pm  Pe  Pa
dt 2
J r
(2.11)
The inertia constant as:
H
J s2
Stored kinetic energy at synchronous speed in mega - joules

Generator MVA rating
2S rated
(2.12)
Changing (2.12) in (2.10) then,
2H
S rated
 s2
d 2
r 2  Pm  Pe  Pa
dt
(2.13)
In steady state, the angular speed of machine is equal to the synchronous speed and we can
replace r in the last Equation by s. In (2.13) Pm, Pe and Pa are offered in MW, so
dividing both sides by the generator MVA rating S rated, then the quantities in per
unit.(2.13).
2 H d 2
 Pm  Pe  Pa
s dt 2
per unit
(2.14)
10
2.4 Multi-Machine Transient Stability
For transient stability, for guess the critical clearing time is significant. When a system
fault happens, the fault should be cleared before the system can under unstable. In a multimachine generator system under a transient, every generator can oscillate, and the
difficulty of calculating the system performance during a transient increases with the multi
-generators (Grainger and Stevenson, 1994).
The simple way for the analysis of a multi- generators power system for transient stability
studies, we have the following steps that were discussed in and (Anderson and Fouad,
1997).

During the transient, the machine power for all generators is constant.

Damping power is ignored.

Every generator is modeled as a fixed transient reactance in series with a fixed
internal voltage.

The angle of each internal voltage is equal to the rotor angle of every generator.

Each load is modeled as a constant reactance, equal to its pre-fault value.

Machines belonging to the same station(brothers-machines) swing together and
are well-knit. A group of coherent machines is represented by one equivalent
machine (Gafari et al., 2013).
And for transient stability analysis has the following steps: (Saadat, 1999).
1. Before the system occur fault, solve the load flow Equations to determine the
initial value.
2. The way followed the network model before fault, decide the system during
fault and for the post-fault case.
3. Solve the swing Equations and calibrate if the system is stable or unstable.
.
In power system under transient stability and through the system we looking for point to
Improving power system stability includes the next cases:

Increasing capacity of transmission lines with multi-line during pre-fault
conditions.

Quick fault clearance, promote transient stability limits.

Fast circuit breaker re-close, increases transmission system capacity in the postfault state and improve transient stability.
11

Increased mechanical inertia of generators, decreases angular acceleration,
slows down rotor angle oscillations, and so increases CCT.
2.5 The Swing Equations For Multi Machine System
Directly, the equal area criterion with the multi machine system cannot be used in power
systems where multi generators are synchronized. It was discussed in (Grainger and
Stevenson,1994). The calculation of (Y) matrix for each grid condition as pre fault, during
and after fault. The numbers (n) of generators, the nodal Equation can be written as:
In
0
=
Ynn
Yrn
Ynr
Yrr
Vn
Vr
(2.15)
The n used to denote generator nodes and the r is used for the remaining nodes. The
Equation (2.15), will be
In = Ynn Vn + Ynr Vr
(2.16)
0 = Yrn Vn + Yrr Vr
(2.17)
In = Ynn − Ynr Vrr −1 + Yrn Vn
(2.18)
Then can be written as
YR = ( Ynn − Ynr Vrr −1 + Yrn )
(2.19)
For the power system during study, the reduced matrices are calculated. Appendix D show
the results matrices before, during and after fault. The power into the grid at node i, that is
the electrical power output of unit i, is given by (Anderson and Fouad, 1997).
n
Ei Ej Yij cos θij − δi + δj
Pei = Ei Gii +
i = 1,2,3 … . n
(2.20)
n =1
n ≠1
Where ,
Yij = Yij θij = Gij + JBij
(2.21)
Negative of the admittance between nodes i and j
Yii = Yii θi = Gii + JBii
(2.22)
12
The Equations of motion are
2Hi
wR
dωj
+Di ωj = Pmi
dt
n
2
− Ei Gii +
Ei Ej Yij cos θij − δi + δj
(2.23)
n=1
n≠1
𝐝𝛅𝐢
= wi − wR
dt
i=1.2.3
n
2
Pmi 0 = Ei Gii0 +
Ei Ej Yij0 cos θij0 − δi0 + δj0
i = 1,2,3 … . n
(2.24)
n=1
n≠1
The 0 here is used to point out the pre-transient conditions. As the network is changed by
circuit breaker during the fault, and The critical clearing time (CCT) is
𝑡 𝑐𝑟 =
4𝐻
( −  0 )
𝑤𝑠 𝑃𝑚 cr
(2.25)
In this thesis, we have considered three machines, and to analysis if the system stable or
unstable. The rotor angles for machines are:
 21 =  2 −  1
(2.26)
 31 =  3 −  1
(2.27)
2.6 Single-Line-To-Ground Fault
The sequence networks and the sequence circuits, the steps for calculating the fault current
under unsymmetrical faults. For the computation of fault currents, we need the following
cases, it was discussed (Grainger and Stevenson, 1994). The cases:
1. Before the fault the power system is balanced, only the positive sequence
network is active. When the fault applies, the sequence networks are connected
only through the fault location.
2. The fault current is ignored such that the before fault positive sequence voltages
are same at all nodes and at the fault location.
13
3. All the grid line charging capacitances and resistances are negligible.
4. All loads are passive except the rotating loads (motors) that are represented by
synchronous machines.
The faulted network as shown in Figure. 2.3 where the voltage at the faulted area will be
known by Vf and current in the three faulted phases are I fa, Ifb and I fc. We will research
how the three sequence networks are connected under the single phase fault condition.
Figure 2.3: Single-line-to-ground fault
The single phase fault has occurred at point (k) of a grid. shown in Figure. 2.4 where it is
supposed that phase-a has contact the ground via an impedance Zf. In this thesis we
suppose that the fault
impedance
is low. Since the system is unloaded before the
occurrence of the fault, we have
IfB = IfC = 0
(2.28)
Figure 2.4: Single phase fault
14
The phase-a voltage at the fault is
Vka
Z f Ifa
=
Ifa =
Ifa0
1
3
=Ifa1 =
(2.29)
1 1
1 a
1 a2
Ifa2
=
1
a2
a
Ifa
0
0
(2.30)
Ifa
3
(2.31)
For the single phase fault the three sequence currents are in series. To signify the zero,
positive and negative sequence Thevenin impedance at the faulted area as Zkk0, Zkk1 and
Zkk2. The voltage at the faulted phase is Vf, we have three sequence circuits that are the
same shown in Figure 2.5 the Thevenin equivalent of the sequence network. So,
Vka 0
=−
Vka 1
=
Vka 2
=−
Vka
=
Zkk 0 Ifa0
(2.32)
Vf − Zkk 1 Ifa1
Zkk 2 Ifa2
Zf Ifa = Zf
Ifa0 =
(2.33)
(2.34)
Ifa0 + Ifa1 + Ifa2
Zkk 0 + Zkk 1
= 3 Zf Ifa0
Vf
+ Zkk 2 + 3 Zf
Figure 2.5: Thevenin equivalent of the sequence network
15
(2.35)
(2.36)
The analysis of synchronous generator by mathematical model is the basis for qualitative
analysis of a synchronous generator and its system stability, which consist of the flux
Equation and voltage Equation, and the rotor motion Equation indicating the torque and
rotor speed change (Ying and Jian, 2013). Its six order mathematical model is as follows:
𝑇𝐽
dω
= Mm − Mc − D ω − ω 0
dt
(2.37)
where,
TJ is Generator inertia constant
dδ
= ω − ω0
dt
(2.38)
For synchronous reactance, transient reactance and sub-transient
T’do
dE’q
= dEfd − Xd − X’d Id − E’q
dt
(2.39)
𝑇’’𝑑0
𝑑𝐸’’𝑞
𝑑𝐸’𝑞
= −𝐸’’𝑞 − 𝑋’𝑑 − 𝑋’’𝑑 𝐼𝑑 + 𝐸’𝑞 + 𝑇’’𝑑0
𝑑𝑡
𝑑𝑡
(2.40)
𝑇’𝑑0
𝑇’’𝑞0
𝑑 𝐸’𝑞
𝑑𝑡
= −𝐸’𝑞 + 𝑋𝑑 − 𝑋’𝑑 𝐼𝑞
(2.41)
𝑑𝐸’’𝑑
𝑑𝐸’𝑑
= −𝐸’’𝑞 − 𝑋’𝑞 − 𝑋’’𝑞 𝐼𝑞 + 𝐸’𝑑 + 𝑇’’𝑞0
𝑑𝑡
𝑑𝑡
(2.42)
2.7 Transient Stability
The methods is used in Chapter 4 with power-world simulator.
A set of differential Equations:
2.43
dx /dt = f(x ,y)
16
A set of algebraic Equations:
(2.44)
g(x ,y) = 0
X: variables are dynamic state variables and Y: variables are bus voltage and angle.
The solutions of the system by these Equations are to determine the electromechanical of
the power system at any time (Wang et al., 2008). Equations (2.43) and (2.44) were solved
by a partition solution method or a simultaneous solution method. In the partitioned
solution method, the differential Equations are solved by a standard numerical integration
method with algebraic Equation (2.44) being solved one by one during time step, was
discussed in (Martins and Lima, 1990). The simultaneous solution employs implicit
integration methods to change the differential Equations of (2.43) into a set of algebraic
Equations which are joint with the algebraic network Equations of (2.44) to be solved as
one set of simultaneous algebraic Equations solutions (Gafari et al., 2013). Appendix E
shows the program for the transient stability solution.
The basics of analysis systems to improve transient stability. We suppose a constant
impedance load and that the system can take in constant power during a fault. We studied
and considered the direct impact of the CCT for Single-line-to-ground fault, the power to
the load during a fault and the trajectories of rotor angle (during pre-fault, fault, and postfault) conditions.
17
CHAPTER 3
RESPONSE SYSTEMS
3.1 Response Systems
The power control system is such as excitation system model, automatic voltage regulator
(AVR), power system stabilizer (PSS) and the governing system. The Study focuses on
the mathematic models of AVR and PSS which can increase the stability of the generator.
The Figure 3.1 shows the power control system structure.
Figure 3.1: The system structure (Tang, 2011)
The power control system let the system go back to the case of stability. By the quick
response to control the generator output voltage, and speed of unit and to increase the
damping ratio to generator to increase the stability after disturbance. The power control
system consists of unit, the AVR, and PSS.
3.2 Generation Control Systems
The generator receives the mechanical power (Pm) from the turbine or mover. The control
signal to the rotor field voltage EFD generated by the AVR that regulates the magnetic
field and to maintain the output voltage of the generator. The stator and the power
network are connected by the step transformer to supply power to the network. The
Figure 3.1 shows that there is one input and three outputs. The input is the control signal
EFD from AVR output. The three outputs go to be feedback signal to the control system
voltage output, current and rotor rotational speed (ω). The signals of voltage and current
18
crosses the control system through the transducer and get out to PSS as the electrical
power (Pe). The rotor speed ω and electrical power (Pe) are the input signal to the PSS to
estimate the power change due to the possible rotor speed oscillation induced by oscillation
disturbance from the power network. After oscillation is applied, PSS is expected to
increase the damping ratio of the closed-loop system so as to damp out or reject the
oscillation disturbance from the power network.
3.2.1 Governing System
The turbine governing system is the responsible of the power system which controls the
input to the turbine to control the generator speed and the active power to response the
demand. The turbine governing system lets the machine able to start up, reach its
operational speed and operate with the required power output. The turbine governing
system controls the mechanical input power (Fuel), so that the power input is reduced as
the speed increases, before the synchronization, and control the mechanical torque after the
synchronization. This way the balance between the input and output power is maintained.
The types of governing system such as steam , gas and hydro turbines. In Chapter 4,
simulations and results study focuses on hydro power plant. A functional diagram of a
standard hydraulic turbine governing system is shown in Figure 3.2.
Figure 3.2: Block diagram of hydraulic turbine governing system.
The most important difference between the hydro turbine governing system and the gas,
steam turbine governing systems, is that a higher power is wanted to reset the control gate,
as the water pressure and the frictional forces are high. In Figure 3.2 the feedback loop
19
with the transient droop, allows the water flow to control the changes in the gate position
(Loen,2014). Turbine governing system model is considered in Chapter 5 as simulations
and results.
3.2.2 Exciters
There are three types of exciters, DC exciters, AC exciters and static exciters, and in this
thesis we focused in AC exciters type ACA1 and static exciters type STA1.
3.2.2.1 AC Exciters (Brushless)
In Figure 3.3 AC exciter is three phase synchronous generators, consisting of a rotating
armature and stator field.
Figure 3.3: A.C. Exciter (Kundur, 1994)
The output is rectified by solid-state rectifier located on the same unit on the shaft rotating
and the output go directly to fed of the machine’s field winding. The stator field winding of
the AC exciter is controlled from the AVR. AC exciter model is suitable for power system
stability studies (Taborda, 2010). The specifications of AC exciter by the following:
1. No brushes in the exciter.
2. Work together of a single machine on the unit with the same shaft.
3. Medium time response in Vf, as only one transient time constant delays the
response, the static power converter delay is small in comparison.
20
3.2.2.2 Static Exciters (Brushed)
This type of exciter is controlled by rectifiers directly supplying the field winding of the
SG via brushes.
Figure 3.4: Static Exciter (Kundur, 1994)
The controlled rectifier is supplied from a power transformer connected that is feeding
from network. Static power electronics exciters are fast voltage response, but still the time
constant of the SG delays the field current response. Figure 3.4 show system structure.
3.2.2.3 Over Excitation Limiter (OEL)
The limiter is used to set the level current into the SG field. A short fixed time delay is
used to let the excitation system to supply maximum field voltage while induced currents
flow during faults. Usually, at the beginning of operation and before connecting via
system ,this limiter is lower point. Without time delay is used under those cases. This
limiter usually uses lower set points when the machine is offline.
3.2.2.4 Under Excitation Limiter (UEL)
An under excitation limiter (UEL) is used to limit the levels of reactive current flowing
into the generator. More specifically, protect the machine as work as motor. Generally this
limiter has been used for of two aims. The first, the loss of field relay, to protect the
machine from loss of synchronism with the power system. The second has been to protect
the generator against overheat due to an extreme increase in under excited vars.
21
3.2. 3 Automatic Voltage Regulator (AVR)
The main purpose of the AVR is to control the output voltage (Vg), of the generator, with
the control signal EFD or the rotor field. The AVR consists of the PID controller and
exciter. The block diagram of the AVR is shown Figure 3.5.
Figure 3.5: The block diagram of the AVR (Tang, 2011)
The Vg is feedback to the system, Vref is the set-point voltage, and Vs is the feedback
from the PSS. The output E FD is the voltage across the rotor winding that induces the
magnetic field so as to control the output voltage (Vg), of the generator. The exciter side
with Vp the constant power source voltage that is controlled with the PID output voltage
to increase the voltage EFD high enough to create the rotor's magnetic field. The result of
the PID output and Vp has to be low pass filtered to clear any noises to being used as the
control signal. The parameters of the exciter TA, KE, TE and SE, the ideal value TA= 0,
and all other parameters is different from station to another station which cannot be
changed. The signal model for AVR in Laplace domain is:
𝐸𝐹𝐷 = 0.0069𝐾𝐺. 𝑉𝑃. 𝐺𝐸𝑋𝐶 𝑆 . 𝐾𝑃 +
𝐾𝐼
𝑆𝐾𝐷
+
. VREF + VS − Vg
𝑆 1 + TD
(3.1)
Vp serves as an amplification gain, KG loop gain of AVR.
𝐺𝐸𝑋𝐶 𝑆 =
1
𝑆𝑇𝐸 + 𝐾𝐸 + 𝑆𝐸
(3.2)
22
𝐺𝐸𝑋𝐶 is the transfer function of the exciter that depends on the body of the exciter and can
be changed in traditions. When PSS is not installed, Vs = 0. In this case, the AVR
regulates only the output voltage Vg. When PSS is installed, AVR needs to help to
increase the damping ratio of the close loop system (Muriithi and Nyakoe, 2015).
3.2. 3.1 Type AC1A Excitation System Model
It belongs to the AC exciters family. The block shown in Figure 3.6 the field-controlled
alternator-rectifier excitation systems type AC1A. This excitation system have an
alternator main exciter (MX) with non-controlled rectifiers. The voltage regulator power is
supplied from a source that is not influenced by outer transients. The diode in the exciter
output force a lower limit of zero on the exciter output voltage.
Figure 3.6: Type AC1A excitation system model
For large power system stability studies, the excitation system of generator can be
explained by the simplified block shown in Figure 3.6. The demagnetizing effect of load
current IFD, on the excitation output voltage VE, is passed as a feedback channel that
includes the constant KD. This constant is a function of the exciter alternator synchronous
and transient reactance (IEEE Standard 421.5, 2005, 2006). The Exciter output voltage
drop is simulated by both of the constant KC and the rectifier regulation curve FEX. Data
in Appendix B.
23
3.2. 3.2 Type ST1A Excitation System Model
The type ST1A power-source controlled-rectifier excitation system shown in Figure 3.7 is
designed to represent systems that the excitation power is supplied via a power
transformer. This transformer on line with the same network, and is regulated by a
controlled rectifier (IEEE Standard 421.5, 2005, 2006). The exciter time constants are
very small, and exciter stabilization may not be needed. Successfully, it may be eligible to
make smaller the transient gain of these systems for other reasons. The block shown is
multilateral to represent transient gain reduction performed either in the forward channel
through time constants, TB and TC (in normal KF = 0), or in the feedback channel by
compatible choice of rate feedback parameters, KF and TF. Voltage regulator gain and any
excitation system time constant are given by KA and TA. The time constants, TC1 and TB,
allow for the chance of transient gain increase, always TC1 should be greater than TB1.
The firing angle for the bridge rectifiers is took affects the input-output relationship, that is
supposed to be linear in the model by choice of a simple gain, KA. For plenty of systems a
really linear relationship applies. In a some systems, the bridge relationship is not linear,
leaving this nominally linear gain a sinusoidal function, the amplitude of that may be
dependent on the voltage supply.
Figure 3.7: Type ST1A excitation system model (Pajuelo et al., 2010)
As the gain is usually set very high, sometimes the limits on VI can be ignored. The
exemplification of the field voltage positive limit as a linear function of synchronous
generator. The negative limit would have a similar current, the sign could be either positive
24
or negative depending about whether a constant firing angle or constant extinction angle is
selected for the limit. As field current is usually low under this condition. As a result of the
high capability, a field current limiter is sometimes used to keep the generator rotor and
exciter in safety level. The limit start setting is known by ILR and the gain is known by
KLR. And have to be to allow KLR = 0. This limiter is illustrated here to keep unity with
the original ST1A over-excitation and under-excitation limiters. In (Kawkabani et
al.,2013). Usually, of these excitation systems, a completely controlled bridge is used, the
model is also serviceable to systems with only half of the bridge is controlled, in this case
the negative field voltage limit is set to zero (VRMIN = 0). Data in Appendix B.
3.2.4 Power System Stabilizer (PSS)
There are many oscillation are occurred in power systems and they usually are applied by
the power network. There are three different oscillations occur in power generators and
transmission networks. They are local mode oscillations (0.7-2Hz), inter unit oscillations
(1-3Hz), and inter area oscillations about (0.5Hz). These frequency oscillations, maybe let
the AVR to react and exporting the oscillation to rotor angle of the synchronous generator
that may result in serious outcomes such as tripping the unit from the grid (Tang, 2011).
Practically, the AVR without external support is not suitable to treat the oscillation.
Perhaps the AVR can be a cause of the problem to rotor angle oscillation. Oftentimes rotor
angle oscillation can be minimized by the damping torque. But if a enough damping torque
is not occurred, the result can be increasing the rotor angle oscillation. the angle change
rate of the rotor speed change △ω overtop to 180◦, the generator will lose the synchronism
that will cause shutdown by protective equipment. The disturbance in the other system,
due to the loss of generation, may cause units tripping. So, it is very important to raise the
damping torque or damping ratio of the closed-loop system to minimize the rotor angle
oscillation. The rotor angle oscillation is the result of rotor speed change. The IFD is the
current in rotor winding and △IFD is the rate of change the current of the rotor field. The
PSS is very important, that is try to reject the oscillation from the power network and to
stop The effect at the rotor speed or angle. Because the signals of PSS and AVR are
feedback controllers, it is important to confirm that they need to be designed together in
order to optimize the power feedback control system and to complete the aim of damping
out the rotor angle oscillation and the aim of voltage regulation with each other. The
analysis of IFD, the signal △ω is necessary to the controller to increase the damping ratio
25
of the closed-loop system. But in case, if AVR work without external support, △ω cannot
be feedback, because the signal of voltage Vg alone has not got any data of △ω. So the
way here is to use PSS to guess △ω and feedback it to minimize the oscillations of the
rotor angle and lead Vs such as input signal to the AVR. As a result, by using PSS and
AVR with each other, closed-loop system damping ratio can be increased and the rotor
angle oscillation can be minimized. And in this thesis we focus on power based stabilizer.
3.2.4 .1 Type PSS1A Power System Stabilizer Model
Figure 3.8 shows the PSS with a single input. The common stabilizer input signals VSI are
frequency, speed and power (IEEE Standard 421.5- 2005, 2006).
Figure 3.8: Type PSS1A power system stabilizer model
T6 be used to be a symbol for a transducer time constant. Stabilizer gain is KS. The signal
washout is put by the time constant T5. The A1 and A2 let some of the low-frequency
impacts of high-frequency filters. The next two models allow two periods of lead-lag
compensation, as set by constants T1 to T4. Stabilizer output can be limited in different
ways. This block shows simple stabilizer output limits, VST MAX and VSTMIN. For some
systems. The stabilizer output VST is an input to the additional control models. Data in
Appendix B.
3.2.4 .2 Type PSS2A Power System Stabilizer Model
The minimization in other oscillation stabilizer designs have lead to the development of a
stabilizer based on the integral of accelerating power (Pa). This type of stabilizer is IEEE
26
standard well-known stabilizer PSS2A (IEEE Standard 421.5, 2005, 2006). The aim of
compensating generator active power change to hold back an negative stabilizing signal
from occurring in conditions. The primary analysis of stabilizer PSS2A merge electrical
power with mechanical power, to get the integral of accelerating power. With speed and
active power. The IEEE standard PSS2A block used for showing this stabilizer design in
Figure 3.9. The fundamental of PSS2A stabilizer works with the synchronous machine
motion Equation (3.3).
1
∆ω = T
(∆Pm − ∆Pg )dt
m
(3.3)
∆Pm dt = Tm ∆w t + ∆Pg dt
(3.4)
The PSS2A stabilizer uses Equation (3.4) to receive a signal proportional to the mechanical
power deviation integral by inserting signals proportional to speed deviation and the
electrical active power deviation integral. As signal may have torsion modes and it is
needful to involve a low-pass filter to clear oscillation torsion modes. The integral of
accelerating power, when Equation (3.4) is added Equation (3.5), the integral of
accelerating power is assigned to rotation speed deviation and generator active power
deviation.
1
Tm
1
1
∆Pa dt = G t ∆w t + Tm
∆Pg dt − Tm
∆Pg dt
(3.5)
The G(t) is the low-pass filter transfer function. Equation (3.5), in the Laplace domain
determines the compute of the integral of accelerating power using rotor speed and
electrical active power values.
1 ∆P a (s)
s
Tm
1 ∆P g (s)
= − Tm
s
+G s
1 ∆P g (s)
Tm
s
+ ∆w(s)
(3.6)
The G(s) is the low-pass filter transfer function. The case with G(s) =1, stabilizer PSS2A is
equivalent to phase minimal stabilizer with a rotor speed input signal. During the case of
G(s) = 0, the stabilizer PSS2A turn into an active power input stabilizer (Sumina et al.,
2011). In spite of the fact that stabilizer PSS2A has a lot of benefit over a single input
27
stabilizer, it is sensitive to the relations between rotor speed and active power. If the
adjustments are to be favorable, two signal channel 1and 2 in Figure 3.9, should be tuned
with estimate to gain and time constants of the filter. Active power signal channel 2,
Figure 3.9 contains models for the derivation of electrical active power deviation integral
(Sumina et al., 2011).
1
∆P g (s)
Tm
s
=
sT W
K s2
1+sT W
1+sT 7
Pg
(3.7)
Figure 3.9: Type PSS2A power system stabilizer model (Lee et al., 2006).
The both signal △ω the output from channel 1 and
got together. then the result is
∆𝑃𝑚
2𝐻𝑆
∆𝑃𝑒
2𝐻𝑆
the output from channel 2 are
then this mixed signal passes the ramp filter, and the
∆𝑃
end result is the integral-of-accelerating power signal 2𝐻𝑎
𝑆
The aims of this power control systems, is initially to keep the generator output voltage,
stable at the set point. Secondly, is to minimize the rotor oscillation, to keep the generator
output stable, by the automatic voltage regulator. And to minimize the rotor angle
oscillation, we involve PSS to damping out the rotor angle oscillation and give reference
signal Vs to AVR to raise closed-loop system damping ratio.
28
CHAPTER 4
RESULTS AND DISCUSSIONS
4.1 Power System Simulation And Models
The main target of this thesis is analysis study and the effect of the AC1A and ST1A
excitation systems. Type PSS1A Power System Stabilizer, type PSS2A Power System
Stabilizer are chosen, for transient stability analysis using the electrical power system
design and analysis simulation power-world 18. The aim of performing transient stability
on the power system is to study the stability of a system under disturbances (phase to
ground fault with solid impedance).
In this Chapter, we have considered multi-machine, nine-bus system shown in Figure 4.1.
This system was discussed in references (Nallagalva et al., 2012), and widely used in the
literatures. The base MVA is 100, and system frequency is 60 Hz. The system data are
given in Appendix A. The system has been simulated with a classical model for the
generators. The disturbance here is the transient by a single-phase fault occurring at
approximately in the middle of line 5–7. The fault is cleared by opening line 5–7
(Anderson and Fouad, 1997). Two types of excitation system models, AVR and PSS were
compared and these models are shown in Table 4.1.
Looking for the best response
situation and health points. The fault in the system may be going to instability and the
units will loses the synchronism. If the system can keep operation until the fault is
cleared, then the all system will be in stable. Through the instability not only the swing in
rotor angle for the final position continue increasing, but also the variation in angular
speed. In such a case the system will not come to its final position. The unbalanced status
or transient condition may go to instability where the units in the power system fall out of
synchronism and may be all the system will black out.
29
Figure 4. 1: Multi-machine, 9-bus system, all impedances are in pu -100MVA base
4.2 The Effect Of Fault Location And Fault Clearing Time
There are some important and influential factors in the study. For all cases, the fault
location is 40% during tests were considered.
To analysis the impact of fault clearing time on transient stability, a disturbance in the form
of a phase to ground fault was simulated. The critical clearing time, which is a criterion of
the stability in power system, depends on the fault clearing times. The stability and
instability of the power system at a given fault is decided by the actions of the generators
in the system. If the rotor angles of the machines diverge, the system is unstable, and if
otherwise the system is stable.
30
4.3 The Comparative Method
In this work, the differences between rotor speed, stator voltage output, rotor angle and
excitation voltage output will be studied. The Table 4.1 will be followed step by step to
analysis IEEE 9 Bus system using power-world simulator will be used.
.
Table 4.1: Excitation System Models, AVR and PSS
Case 1:
Case 2:
Type ST1A excitation system model
Type ST1A excitation system model
Type PSS1A Power System Stabilizer
Without Stabilizer
fault cleared at time, t = 0.1 second
fault cleared at time, t = 0.1 second
Fault Location 40 % between bus 5-7
Fault Location 40 % between bus 5-7
Case 3:
Type ST1A excitation system model
Type PSS2A Power System Stabilizer
fault cleared at time, t = 0.1 second
Fault Location 40 % between bus 5-7
General
fault resistance = solid
Governor IEEEG1
Cycles =240--246
Case 4:
Type AC1A excitation system model
Type PSS1A Power System Stabilizer
fault cleared at time, t = 0.1 second
Fault Location 40 % between bus 5-7
Case 5:
Type AC1A excitation system model
Without Stabilizer
fault cleared at time, t = 0.1 second
Fault Location 40 % between bus 5-7
Case 6:
Type AC1A excitation system model
Type PSS2A Power System Stabilizer
fault cleared at time, t = 0.1 second
Fault Location 40 % between bus 5-7
General
fault resistance = solid
Governor IEEEG1
Cycles =240--246
4.4 Power-World
The Y-matrix for each network condition (pre-fault, during and after fault) is calculated. In
a power system with multi-generators, the nodal Equations in Chapter 2. Sequence data
for all devices such as generators, transmission lines, transformers and loads.
31
1- Before Fault
Bus 2
Bus 7
Bus 8
Bus 9
Bus 3
163 MW
7 Mvar
85 MW
-11 Mvar
100 MW
35 Mvar
Bus 5
Bus 6
125 MW
50 Mvar
90 MW
30 Mvar
Bus 4
Bus1
slack
72 MW
27 Mvar
Figure 4. 2: Multi-machine, 9-bus system before-fault with POWER-WORLD
54.14350
54.14300
54.14250
54.14200
54.14150
54.14100
54.14050
54.14000
54.13950
54.13900
54.13850
54.13800
54.13750
54.13700
54.13650
54.13600
54.13550
54.13500
54.13450
54.13400
54.13350
54.13300
61.105500
61.105000
61.104500
61.104000
61.103500
61.103000
61.102500
61.102000
61.101500
61.101000
61.100500
61.100000
61.099500
61.099000
61.098500
61.098000
61.097500
61.097000
61.096500
61.096000
61.095500
61.095000
61.094500
61.094000
3.586200
3.586150
3.586100
3.586050
3.586000
3.585950
3.585900
3.585850
3.585800
3.585750
3.585700
3.585650
3.585600
3.585550
3.585500
0
1
2
3
4
5
6
b
c
d
e
f
g
7
8
9
10
11
12
13
14
Rotor Angle_Gen Bus1 #1 g
b
c
d
e
f
15
16
17
18
19
20
Rotor Angle_Gen Bus 2 #1 g
b
c
d
e
f
Figure 4.3: Rotor angle before fault
32
21
22
23
24
25
26
Rotor Angle_Gen Bus 3 #1
27
28
29
30
60.006000
60.005500
60.005000
60.004500
60.004000
60.003500
60.003000
60.002500
60.002000
60.001500
60.001000
60.000500
60.000000
59.999500
59.999000
59.998500
59.998000
59.997500
59.997000
59.996500
59.996000
59.995500
59.995000
59.994500
59.994000
60.006000
60.005500
60.005000
60.004500
60.004000
60.003500
60.003000
60.002500
60.002000
60.001500
60.001000
60.000500
60.000000
59.999500
59.999000
59.998500
59.998000
59.997500
59.997000
59.996500
59.996000
59.995500
59.995000
59.994500
59.994000
60.006000
60.005500
60.005000
60.004500
60.004000
60.003500
60.003000
60.002500
60.002000
60.001500
60.001000
60.000500
60.000000
59.999500
59.999000
59.998500
59.998000
59.997500
59.997000
59.996500
59.996000
59.995500
59.995000
59.994500
59.994000
0
1
2
3
4
5
6
7
8
9
b
c
d
e
f
g
10
11
12
13
14
Speed_Gen Bus1 #1 g
b
c
d
e
f
15
16
17
18
19
20
Speed_Gen Bus 2 #1 g
b
c
d
e
f
21
22
23
24
25
26
27
28
29
Speed_Gen Bus 3 #1
Figure 4.4: Speed before fault
1.403100
1.789460
1.082240
1.403080
1.789440
1.082230
1.403060
1.789420
1.082220
1.789400
1.403040
1.082210
1.082200
1.789380
1.082190
1.403020
1.789360
1.082180
1.403000
1.789340
1.082170
1.402980
1.789320
1.789300
1.402960
1.082160
1.082150
1.082140
1.789280
1.082130
1.402940
1.789260
1.082120
1.402920
1.789240
1.082110
1.402900
1.789220
1.789200
1.082100
1.082090
1.082080
1.402880
1.789180
1.082070
1.402860
1.789160
1.082060
1.789140
1.082050
1.402840
1.789120
1.082040
1.082030
0
1
2
3
4
5
b
c
d
e
f
g
6
7
8
9
10
11
12
13
Field Voltage (pu)_Gen Bus1 #1 g
b
c
d
e
f
14
15
16
17
18
19
20
Field Voltage (pu)_Gen Bus 2 #1 g
b
c
d
e
f
21
22
23
24
25
26
27
28
29
30
Field Voltage (pu)_Gen Bus 3 #1
Figure 4.5: Excitation before fault
2- During Phase To Ground Fault Between Bus 5—7 Location 40%
Bus 2
Bus 7
Bus 8
Bus 9
163 MW
7 Mvar
Bus 3
85 MW
-11 Mvar
85.7 MW
86.6 MW 85.7 MW
84.3 MW
Bus 5
100 MW
35 Mvar
Bus 6
125 MW
50 Mvar
90 MW
30 Mvar
Bus 4
Bus1
slack
72 MW
27 Mvar
Figure 4.6: Multi-machine, 9-bus system during-fault With POWER-WORLD
33
30
3- After Fault Cleared
A phase to ground fault short circuit is added in the line 5-7. The fault happens at 4 second
and the circuit breakers operate at 4.1 second, t = 0.1 s. The total simulation time is 30
seconds, time step is 0.008 s.
Bus 2
Bus 7
Bus 8
Bus 9
Bus 3
163 MW
21 Mvar
85 MW
13 Mvar
Bus 5
100 MW
35 Mvar
Bus 6
125 MW
50 Mvar
90 MW
30 Mvar
Bus 4
Bus1
slack
80 MW
82 Mvar
Figure 4.7: Multi-machine, 9-bus system after-fault With POWER-WORLD
34
Case 1:

Rotor speed
Figure 4.8 show the rotor speed during the fault for Case 1. It can be seen in the
plots that the highest oscillation are for unit 1 is 60.25 to 59.8 HZ, unit 2 is 60.3 to
59.7 HZ and unit 3 is 60.2 to 59.8 HZ. It takes approximately 10 seconds after the
fault occurrence to return to steady state.

Stator voltage
Figure 4. 11 show the stator voltage during the fault for Case 1, the voltage
oscillation close for unit 1 from 1.09 to 0.97 pu , for unit 2 from 1.24 to 0.92 pu,
and for unit 3 from 1.16 to 0.88 pu during the fault and it start to recover after the
operation of the circuit breakers to clean the fault. approximately 10 seconds after
the fault occurrence to return to steady state.

Rotor angle
Figure 4.10 show the rotor angle during the fault for Case 1, the rotor angle
oscillated close for unit 1 from 8◦ to -28◦, for unit 2 from 86◦ to 58◦, and for unit
3 from 59◦ to 49◦.

Excitation
Figure 4.9 show the stator voltage during the fault for Case 1, the support voltage
for unit 1 from 1.6 to 0.65 pu, for unit 2 from 2.5 to 1.3 pu , and for unit 3 from
2.2 to 0.9pu return to steady state. approximately 10 seconds.
60.25
60.2
60.15
60.3
60.25
60.2
60.1
60.2
60.15
60.15
60.1
60.05
60.1
60.05
60.05
60
60
60
59.95
59.95
59.95
59.9
59.9
59.85
59.9
59.85
59.8
59.8
59.75
59.85
59.75
59.7
59.8
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Speed_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
Speed_Gen Bus 3 #1
Figure 4.8: Case 1-ST1A with PSS1A
35
22
24
Speed_Gen Bus 2 #1
26
28
30
2.3
2.5
2.2
1.6
1.55
2.4
1.5
2
2.3
1.45
1.4
1.9
2.2
1.8
2.1
1.35
1.3
2.1
1.7
2
1.6
1.9
1.5
1.8
1.4
1.7
1.3
1.6
1.2
1.25
1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
1.5
1.4
0.8
0.75
1.3
0.7
0.65
1.1
1
0.9
0
2
4
6
8
10
12
g
b
c
d
e
f
b
c
d
e
f
g
b
c
d
e
f
g
14
16
18
20
22
24
26
28
30
24
26
28
30
28
30
Field V oltage (pu)_Gen Bus1 #1
Field V oltage (pu)_Gen Bus 2 #1
Field V oltage (pu)_Gen Bus 3 #1
Figure 4.9: Case 1-ST1A with PSS1A
59
58.5
84
58
82
8
6
57.5
4
80
2
57
56.5
78
56
76
0
-2
-4
55.5
74
-6
55
54.5
72
-8
54
70
-10
68
-12
53.5
53
-14
66
52.5
-16
52
64
51.5
-18
62
-20
60
-22
51
50.5
50
-24
58
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Rotor A ngle_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
Rotor A ngle_Gen Bus 2 #1
Rotor A ngle_Gen Bus 3 #1
Figure 4.10: Case 1-ST1A with PSS1A
1.16
1.14
1.12
1.1
1.24
1.22
1.2
1.18
1.16
1.08
1.06
1.04
1.02
1.14
1.12
1.1
1.08
1.06
1
0.98
1.04
1.02
0.96
1
0.94
0.98
0.92
0.96
0.94
1.09
1.085
1.08
1.075
1.07
1.065
1.06
1.055
1.05
1.045
1.04
1.035
1.03
1.025
1.02
1.015
1.01
1.005
1
0.995
0.99
0.985
0.98
0
2
4
g
b
c
d
e
f
b
c
d
e
f
g
6
8
10
12
14
Bus V olt (pu)_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
Bus V olt (pu)_Gen Bus 3 #1
Figure 4.11: Case 1-ST1A with PSS1A
36
22
24
26
Bus V olt (pu)_Gen Bus 2 #1
Case 2:

Rotor speed
Figure 4.12 show the rotor speed during the fault for Case 2. It can be seen in the
plots that the highest oscillation are for unit 1 is 60.25 to 59.8 HZ, unit 2 is 60.35
to 59.7 HZ and unit 3 is 60.25 to 59.8 HZ. It takes approximately 12 seconds after
the fault occurrence to return to steady state.

Stator voltage
Figure 4.15
show the stator voltage during the fault for Case 2, the voltage
oscillation close for unit 1 from 1.09 to 0.985 pu, for unit 2 from 1.24 to 0.92 pu,
and for unit 3 from 1.16 to 0.9 pu, during the fault and it start to recover after the
operation of the circuit breakers to clean the fault. approximately 12 seconds after
the fault occurrence to return to steady state.

Rotor angle
Figure 4.14 show the rotor angle during the fault for Case 2, the rotor angle
oscillated close for unit 1 from 8◦ to -26◦, for unit 2 from 86◦ to 58◦, and for unit
3 from 59◦ to 50.5◦.

Excitation
Figure 4.13 show the stator voltage during the fault for Case 2, the support voltage
for unit 1 from 1.4 to 0.85 pu, for unit 2 from 2.25 to 1.3 pu, and for unit 3
from 2 to 1 pu return to steady state. approximately 10 seconds.
60.25
60.2
60.35
60.25
60.3
60.2
60.25
60.15
60.1
60.05
60.2
60.15
60.15
60.1
60.1
60.05
60.05
60
60
59.95
59.9
59.95
60
59.95
59.9
59.85
59.9
59.8
59.85
59.85
59.8
59.75
59.75
59.7
59.8
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Speed_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
Speed_Gen Bus 3 #1
Figure 4.12: Case 2-ST1A without - PSS
37
24
Speed_Gen Bus 2 #1
26
28
30
2
2.25
1.9
2.2
2.15
1.4
1.35
2.1
1.8
2.05
2
1.7
1.95
1.3
1.25
1.6
1.9
1.2
1.5
1.85
1.8
1.15
1.75
1.4
1.7
1.65
1.3
1.1
1.05
1.6
1
1.2
1.55
1.5
1.1
1.45
1
1.4
1.35
0.9
1.3
0.85
0.95
0
2
4
6
8
10
12
g
b
c
d
e
f
b
c
d
e
f
g
b
c
d
e
f
g
14
16
18
20
22
24
26
28
30
24
26
28
30
28
30
Field V oltage (pu)_Gen Bus1 #1
Field V oltage (pu)_Gen Bus 2 #1
Field V oltage (pu)_Gen Bus 3 #1
Figure 4.13: Case 2-ST1A without – PSS
59
86
58.5
84
8
6
58
4
82
2
57.5
80
0
56.5
78
-2
56
76
57
-4
-6
55.5
74
55
-8
72
-10
54
70
-12
53.5
68
-14
54.5
53
-16
66
52.5
-18
52
64
51.5
62
-22
51
60
-24
58
-26
50.5
-20
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Rotor A ngle_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
Rotor A ngle_Gen Bus 2 #1
Rotor A ngle_Gen Bus 3 #1
Figure 4.14: Case 2-ST1A without – PSS
1.16
1.24
1.14
1.22
1.12
1.2
1.1
1.18
1.16
1.08
1.06
1.14
1.12
1.04
1.1
1.02
1.08
1
1.06
1.04
0.98
1.02
0.96
1
0.94
0.98
0.92
0.9
0.96
0.94
0.92
1.09
1.085
1.08
1.075
1.07
1.065
1.06
1.055
1.05
1.045
1.04
1.035
1.03
1.025
1.02
1.015
1.01
1.005
1
0.995
0.99
0.985
0
2
4
g
b
c
d
e
f
b
c
d
e
f
g
6
8
10
12
14
Bus V olt (pu)_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
26
Bus V olt (pu)_Gen Bus 2 #1
Bus V olt (pu)_Gen Bus 3 #1
Figure 4.15: Case 2-ST1A without - PSS
38
24
Case 3:

Rotor speed
Figure 4.16 show the rotor speed during the fault for Case 3. It can be seen in the
plots that the highest oscillation are for unit 1 is 60.25 to 59.8 HZ, unit 2 is 60.35
to 59.7 HZ, and unit 3, 60.25 to 59.8 HZ. It takes approximately 12 seconds after
the fault occurrence to return to steady state.

Stator voltage
Figure 4.19
show the stator voltage during the fault for Case 3, the voltage
oscillation close for unit 1 from 1.09 to 0.98 pu, for unit 2 from 1.24 to 0.94 pu,
and for unit 3 from 1.16 to 0.9 pu during the fault and it start to recover after the
operation of the circuit breakers to clean the fault. approximately 12 seconds after
the fault occurrence to return to steady state.

Rotor angle
Figure 4.18 show the rotor angle during the fault for Case 3, the rotor angle
oscillated close for unit 1 from 8◦ to -24◦, for unit 2 from 84◦ to 58◦, and for unit
3 from 59◦ to 50◦.

Excitation
Figure 4.17 show the stator voltage during the fault for Case 3, the support voltage
for unit 1 from 1.6 to 0.65 pu, for unit 2 from 2.4 to 1.3 pu, and for unit 3 from
2.1 to 1pu return to steady state. approximately 10 seconds.
60.25
60.35
60.25
60.3
60.2
60.2
60.25
60.15
60.1
60.05
60.2
60.15
59.95
60.1
60.1
60.05
60
60.15
60
60.05
60
59.95
59.95
59.9
59.9
59.85
59.9
59.85
59.8
59.8
59.75
59.85
59.75
59.7
59.8
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Speed_Gen Bus1 #1
16
b
c
d
e
f
g
Speed_Gen Bus 3 #1
Figure 4.16: Case 3-ST1A with PSS2A
39
18
20
22
24
Speed_Gen Bus 2 #1
26
28
30
2.1
2.4
2
2.3
1.9
2.2
1.8
2.1
1.7
2
1.6
1.9
1.5
1.8
1.4
1.7
1.3
1.6
1.2
1.5
1.1
1.4
1
1.3
1.65
1.6
1.55
1.5
1.45
1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0
2
4
6
8
10
12
g
b
c
d
e
f
b
c
d
e
f
g
b
c
d
e
f
g
14
16
18
20
22
24
26
28
30
24
26
28
30
28
30
Field Voltage (pu)_Gen Bus1 #1
Field Voltage (pu)_Gen Bus 2 #1
Field Voltage (pu)_Gen Bus 3 #1
Figure 4.17: Case 3-ST1A with PSS2A
59.5
8
84
59
58.5
6
82
4
57.5
80
2
57
78
58
56.5
0
-2
76
56
-4
74
55.5
55
-6
72
-8
54
70
-10
53.5
68
54.5
-12
-14
53
66
52.5
-16
52
64
51.5
62
-20
50.5
60
-22
50
58
-18
51
-24
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Rotor A ngle_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
Rotor A ngle_Gen Bus 2 #1
Rotor A ngle_Gen Bus 3 #1
Figure 4.18: Case 3-ST1A with PSS2A
1.16
1.14
1.12
1.1
1.24
1.22
1.2
1.18
1.16
1.08
1.06
1.04
1.02
1.14
1.12
1.1
1.08
1.06
1
0.98
1.04
1.02
0.96
1
0.94
0.98
0.92
0.96
0.94
0.9
1.09
1.085
1.08
1.075
1.07
1.065
1.06
1.055
1.05
1.045
1.04
1.035
1.03
1.025
1.02
1.015
1.01
1.005
1
0.995
0.99
0.985
0.98
0
2
4
g
b
c
d
e
f
b
c
d
e
f
g
6
8
10
12
14
Bus V olt (pu)_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
Bus V olt (pu)_Gen Bus 3 #1
Figure 4.19: Case 3-ST1A with PSS2A
40
22
24
26
Bus V olt (pu)_Gen Bus 2 #1
Case 4:

Rotor speed
Figure 4.20 show the rotor speed during the fault for Case 4. It can be seen in the
plots that the highest oscillation are for unit 1 is 60. 35 to 59.8 HZ, unit 2 is 60.4 to
59.7 HZ, and unit 3 is 60.2 to 59.75 HZ, more continuous oscillation in unit 3, after
the fault occurrence.

Stator voltage
Figure 4.23
show the stator voltage during the fault for Case 4, the voltage
oscillation close for unit 1 from 1.1 to 0.96 pu, for unit 2 from 1.24 to 0.92 pu,
and for unit 3 from 1.16 to 0.86 pu during the fault, and it start to recover after the
operation of the circuit breakers to clean the fault. More continuous oscillation in
unit3, after the fault occurrence.

Rotor angle
Figure 4.22 show the rotor angle during the fault for Case 4, the rotor angle
oscillated close for unit 1 from 10◦ to -30◦, for unit 2 from 88◦ to 58◦, and for
unit 3 from 61◦ to 50◦.

Excitation
Figure 4.21 show the stator voltage during the fault for Case 4, the support voltage
for unit 1 from 3.6 to 0 pu , for unit 2 from 4 to - 0.5 pu, and for unit 3 from 3.4
to 0 pu, more continuous oscillation in unit 3, after the fault occurrence.
60.4
60.2
60.15
60.35
60.3
60.35
60.3
60.25
60.25
60.1
60.05
60.2
60.2
60.15
60.1
60
59.95
60.05
59.85
60.1
60.05
60
59.95
59.9
60.15
59.9
59.85
60
59.95
59.9
59.8
59.8
59.75
59.85
59.75
59.7
59.8
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Speed_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
Speed_Gen Bus 3 #1
Figure 4.20: Case 4-AC1A with PSS1A
41
22
24
Speed_Gen Bus 2 #1
26
28
30
3.4
3.6
4
3.4
3.2
3
3.5
3.2
3
2.8
3
2.8
2.6
2.6
2.4
2.5
2.4
2.2
2
2.2
2
2
1.8
1.8
1.5
1.6
1.6
1.4
1.4
1
1.2
1.2
1
0.5
1
0.8
0.8
0
0.6
0.4
0.6
0.4
-0.5
0.2
0.2
0
0
0
2
4
6
8
10
12
g
b
c
d
e
f
b
c
d
e
f
g
b
c
d
e
f
g
14
16
18
20
22
24
26
28
30
24
26
28
30
28
30
Field V oltage (pu)_Gen Bus1 #1
Field V oltage (pu)_Gen Bus 2 #1
Field V oltage (pu)_Gen Bus 3 #1
Figure 4.21: Case 4-AC1A with PSS1A
61
88
60
86
84
59
58
57
82
80
78
76
56
74
55
72
70
54
53
52
68
66
64
62
51
60
50
58
56
12
10
8
6
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-22
-24
-26
-28
-30
-32
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Rotor A ngle_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
Rotor A ngle_Gen Bus 2 #1
Rotor A ngle_Gen Bus 3 #1
Figure 4.22: Case 4-AC1A with PSS1A
1.16
1.24
1.14
1.22
1.12
1.2
1.09
1.1
1.18
1.08
1.08
1.16
1.07
1.14
1.06
1.12
1.05
1.06
1.04
1.02
1.1
1.08
1
0.98
0.96
1.06
1.1
1.04
1.03
1.02
1.04
1.02
1.01
1
0.94
1
0.92
0.98
0.99
0.9
0.96
0.98
0.88
0.94
0.97
0.86
0.92
0.96
0
2
4
g
b
c
d
e
f
b
c
d
e
f
g
6
8
10
12
14
Bus V olt (pu)_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
Bus V olt (pu)_Gen Bus 3 #1
Figure 4.23: Case 4-AC1A with PSS1A
42
22
24
26
Bus V olt (pu)_Gen Bus 2 #1
Case 5:

Rotor speed
Figure 4.24 show the rotor speed during the fault for Case 5. It can be seen in the
plots that the highest oscillation are for unit 1 is 60. 3 to 59.8 HZ, unit 2 is 60.5 to
59.6 HZ and unit 3 is 60.25 to 59.75 HZ. It takes approximately 12 seconds after
the fault occurrence to return to steady state.

Stator voltage
Figure 4.27
show the stator voltage during the fault for Case 5, the voltage
oscillation close for unit 1 from 1.09 to 0.99 pu, for unit 2 from 1.24 to 0.9 pu,
and for unit 3 from 1.16 to 0.88 pu during the fault, and it start to recover after the
operation of the circuit breakers to clean the fault. Approximately 12 seconds after
the fault occurrence to return to steady state.

Rotor angle
Figure 4.26 show the rotor angle during the fault for Case 5, the rotor angle
oscillated close for unit 1 from 15◦ to -30◦, for unit 2 from 90◦ to 52◦, and for
unit 3 from 59.5◦ to 49◦.

Excitation
Figure 4.25 show the stator voltage during the fault for Case 5, the support voltage
for unit 1 from 2.4 to 0.4 pu, for unit 2 from 4.5 to 0 pu, and for unit 3 from 3.8
to 0.2 pu, approximately 10 seconds to return to steady state.
60.25
60.5
60.3
60.45
60.2
60.4
60.25
60.35
60.15
60.1
60.3
60.25
60.2
60.15
60.2
60.05
60.15
60
60.05
59.95
59.95
60.1
60.1
60
59.9
59.9
59.85
60.05
60
59.95
59.85
59.8
59.9
59.75
59.8
59.7
59.65
59.75
59.85
59.8
59.6
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Speed_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
Speed_Gen Bus 2 #1
Speed_Gen Bus 3 #1
Figure 4.24: Case 5-AC1A without - PSS
43
24
26
28
30
3.8
3.6
2.4
4.5
3.4
3.2
2.2
4
3
2
2.8
3.5
1.8
2.6
2.4
3
1.6
2.2
2
2.5
1.4
2
1.2
1.8
1.6
1.4
1
1.5
1.2
0.8
1
1
0.8
0.6
0.6
0.5
0.4
0.4
0.2
0
0
2
4
6
8
10
12
g
b
c
d
e
f
b
c
d
e
f
g
b
c
d
e
f
g
14
16
18
20
22
24
26
28
30
24
26
28
30
28
30
Field V oltage (pu)_Gen Bus1 #1
Field V oltage (pu)_Gen Bus 2 #1
Field V oltage (pu)_Gen Bus 3 #1
Figure 4.25: Case 5-AC1A without – PSS
59.5
59
58.5
58
57.5
57
56.5
56
55.5
55
54.5
54
53.5
53
52.5
52
51.5
51
50.5
50
49.5
49
90
15
88
86
10
84
82
5
80
78
0
76
74
-5
72
70
68
-10
66
64
-15
62
60
-20
58
56
-25
54
52
-30
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Rotor A ngle_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
Rotor A ngle_Gen Bus 2 #1
Rotor A ngle_Gen Bus 3 #1
Figure 4.26: Case 5-AC1A without - PSS
1.16
1.24
1.14
1.22
1.12
1.2
1.1
1.08
1.18
1.16
1.14
1.06
1.12
1.04
1.1
1.02
1.08
1
1.06
0.98
0.96
1.04
1.02
1
0.94
0.98
0.92
0.96
0.9
0.94
0.88
0.92
0.9
1.09
1.085
1.08
1.075
1.07
1.065
1.06
1.055
1.05
1.045
1.04
1.035
1.03
1.025
1.02
1.015
1.01
1.005
1
0.995
0.99
0
2
g
b
c
d
e
f
b
c
d
e
f
g
4
6
8
10
12
14
Bus V olt (pu)_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
Bus V olt (pu)_Gen Bus 3 #1
Figure 4.27: Case 5-AC1A without - PSS
44
24
26
Bus V olt (pu)_Gen Bus 2 #1
Case 6:

Rotor speed
Figure 4.28 show the rotor speed during the fault for Case 6. It can be seen in the
plots that the highest oscillation are for unit 1 is 60.3 to 59.8 HZ unit 2 is 60.35 to
59.7 HZ and unit 3 is 60.2 to 59.75 HZ. It takes approximately 4 seconds after the
fault occurrence to return to steady state.

Stator voltage
Figure 4.31
show the stator voltage during the fault for Case 6, the voltage
oscillation close for unit 1 from 1.09 to 0.96 pu, for unit 2 from 1.24 to 0.94 pu,
and for unit 3 from 1.16 to 0.9 pu during the fault, and it start to recover after the
operation of the circuit breakers to clean the fault. Approximately 4 seconds after
the fault occurrence to return to steady state.

Rotor angle
Figure 4.30 show the rotor angle during the fault for Case 6, the rotor angle
oscillated close for unit 1 from 10◦ to -26◦ for unit 2 from 86◦ to 58◦ and for unit
3 from 60.5◦ to 49◦.

Excitation
Figure 4.29 show the stator voltage during the fault for Case 6, the support voltage
for unit 1 from 3.2 to 0 pu for unit 2 from 3.4 to 0 pu, and for unit 3 from 3.6
to 0.2 pu, approximately 10 seconds to return to steady state.
60.35
60.3
60.2
60.3
60.15
60.1
60.25
60.25
60.2
60.2
60.15
60.15
60.05
60
60.1
60.1
60.05
60.05
60
59.95
60
59.95
59.9
59.85
59.9
59.85
59.95
59.9
59.8
59.8
59.75
59.85
59.75
59.7
59.8
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Speed_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
Speed_Gen Bus 3 #1
Figure 4.28: Case 6-AC1A with - PSS2A
45
24
Speed_Gen Bus 2 #1
26
28
30
3.2
3.6
3.4
3.4
3.2
3.2
3
3
2.8
3
2.8
2.6
2.8
2.6
2.4
2.6
2.4
2.2
2.4
2.2
2
2.2
2
1.8
2
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1
1
1
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
1.6
1.4
1.2
0
0
2
4
6
8
10
12
g
b
c
d
e
f
b
c
d
e
f
g
b
c
d
e
f
g
14
16
18
20
22
24
26
28
30
24
26
28
30
28
30
Field V oltage (pu)_Gen Bus1 #1
Field V oltage (pu)_Gen Bus 2 #1
Field V oltage (pu)_Gen Bus 3 #1
Figure 4.29: Case 6-AC1A with - PSS2A
60
59
86
10
84
8
82
58
80
57
78
56
76
55
74
72
54
70
6
4
2
0
-2
-4
-6
-8
-10
-12
53
68
-14
52
66
-16
51
50
49
64
-18
-20
62
-22
60
-24
58
-26
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
Rotor A ngle_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
Rotor A ngle_Gen Bus 2 #1
Rotor A ngle_Gen Bus 3 #1
Figure 4.30: Case 6-AC1A with - PSS2A
1.16
1.24
1.09
1.14
1.22
1.08
1.12
1.2
1.1
1.18
1.07
1.06
1.16
1.08
1.14
1.05
1.06
1.12
1.04
1.04
1.1
1.03
1.02
1.08
1.02
1
1.06
1.01
1.04
0.98
1.02
1
0.96
1
0.99
0.94
0.98
0.98
0.92
0.96
0.97
0.9
0.94
0.96
0
2
4
g
b
c
d
e
f
b
c
d
e
f
g
6
8
10
12
14
Bus V olt (pu)_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
Bus V olt (pu)_Gen Bus 3 #1
Figure 4.31: Case 6-AC1A with - PSS2A
46
24
26
Bus V olt (pu)_Gen Bus 2 #1
 The Acceleration :
60
20
50
15
10
60
50
10
0
-10
-20
-10
-15
20
10
0
-10
-20
-30
-30
-40
-40
-50
-50
-20
-60
-25
40
30
5
-5
70
30
20
0
80
40
-60
-70
-70
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
A ccel MW_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
24
26
28
30
28
30
28
30
A ccel MW_Gen Bus 2 #1
A ccel MW_Gen Bus 3 #1
Figure 4.32: Acceleration- ST1A without PSS
60
20
15
10
70
40
60
30
0
-5
10
0
-10
-20
-10
-15
30
20
10
0
-10
-20
-30
-30
-40
-40
-50
-50
-20
-60
-25
50
40
20
5
80
50
-60
-70
-70
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
A ccel MW_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
24
26
A ccel MW_Gen Bus 2 #1
A ccel MW_Gen Bus 3 #1
Figure 4.33: Acceleration- ST1A with PSSA1
60
20
15
10
70
40
60
30
0
-5
-15
20
0
10
-10
0
-10
-20
-30
-30
-40
-40
-50
-50
-20
-60
-25
30
10
-20
-10
50
40
20
5
80
50
-60
-70
-70
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
A ccel MW_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
A ccel MW_Gen Bus 3 #1
Figure 4.34: Acceleration- ST1A with PSS2A
47
22
24
26
A ccel MW_Gen Bus 2 #1
25
70
20
90
80
70
60
50
15
60
50
40
30
20
10
0
-10
-20
-30
-40
40
10
30
5
20
10
0
0
-5
-10
-20
-10
-50
-60
-70
-80
-90
-100
-110
-120
-30
-15
-40
-50
-20
-60
-25
-70
0
2
4
6
8
g
b
c
d
e
f
b
c
d
e
f
g
10
12
14
A ccel MW_Gen Bus1 #1
16
18
b
c
d
e
f
g
20
22
24
26
28
30
28
30
A ccel MW_Gen Bus 2 #1
A ccel MW_Gen Bus 3 #1
Figure 4.35: Acceleration- AC1A without PSS
25
100
60
20
90
80
50
70
40
15
60
50
30
10
40
20
5
30
20
10
10
0
0
0
-10
-10
-5
-20
-20
-10
-30
-40
-30
-50
-40
-15
-60
-70
-50
-20
-80
-60
-25
-70
-90
-100
0
2
4
6
8
g
b
c
d
e
f
b
c
d
e
f
g
10
12
14
16
Accel MW_Gen Bus1 #1
18
b
c
d
e
f
g
20
22
24
26
Accel MW_Gen Bus 2 #1
Accel MW_Gen Bus 3 #1
Figure 4.36: Acceleration - AC1A with PSS1A
60
20
50
90
80
70
15
10
5
40
60
30
50
20
40
10
30
20
0
-5
-10
-15
-20
0
0
-20
-10
-30
-20
-30
-40
-40
-50
-50
-60
-25
10
-10
-60
-70
-70
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
A ccel MW_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
A ccel MW_Gen Bus 3 #1
Figure 4.37: Acceleration- AC1A with PSS2A
48
24
26
A ccel MW_Gen Bus 2 #1
28
30
 Special case the fault cleared t = 0.3 second
The ST1A without - PSS is stable with time fault cleared at time, t = 0.3 second. The
system was able to be stable. But AC1A without-PSS show that with time 0.3s is
unstable. It was clear and were shown from Figure 4.38 to Figure 4.42.
64
62.6
63.5
62.4
63
62.2
62.5
62
62
61.8
61.5
61.6
61
61.4
60
59.5
59
58.5
58
61.2
60.5
57.5
61
60
60.8
59.5
57
60.6
59
56.5
60.4
58.5
60.2
56
58
60
57.5
55.5
59.8
57
59.6
0
2
4
6
8
g
b
c
d
e
f
b
c
d
e
f
g
10
12
14
Speed_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
24
26
28
30
Speed_Gen Bus 2 #1
Speed_Gen Bus 3 #1
Figure 4.38: AC1A without - PSS is unstable with time 0.3s
4.5
4
6.5
6
5.5
5
4.5
3.5
4
3.5
3
3
2.5
2.5
2
1.5
2
1
1.5
0.5
0
-0.5
1
0.5
-1
-1.5
-2
-2.5
0
-3
4.2
4
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
g
b
c
d
e
f
b
c
d
e
f
g
b
c
d
e
f
g
14
16
18
20
22
24
Field Voltage (pu)_Gen Bus1 #1
Field Voltage (pu)_Gen Bus 2 #1
Field Voltage (pu)_Gen Bus 3 #1
Figure 4.39: AC1A without - PSS is unstable with time 0.3s
49
26
28
30
0
13,000
10,500
10,000 12,000 -2,000
9,500
9,000 11,000 -4,000
8,500
10,000
-6,000
8,000
7,500
9,000
-8,000
7,000
8,000
6,500
-10,000
6,000
7,000
5,500
-12,000
5,000
6,000
4,500
-14,000
4,000
5,000
3,500
-16,000
4,000
3,000
2,500
-18,000
3,000
2,000
1,500
2,000 -20,000
1,000
1,000 -22,000
500
0
0 -24,000
0
2
4
6
g
b
c
d
e
f
b
c
d
e
f
g
8
10
12
14
16
b
c
d
e
f
g
Rotor A ngle_Gen Bus1 #1
18
20
22
24
26
28
30
Rotor A ngle_Gen Bus 2 #1
Rotor A ngle_Gen Bus 3 #1
Figure 4.40: AC1A without - PSS is unstable with time 0.3s
60.35
60.3
60.45
60.4
60.4
60.35
60.35
60.3
60.25
60.3
60.25
60.2
60.25
60.2
60.15
60.2
60.15
60.1
60.05
60.15
60.1
60.1
60.05
60.05
60
60
59.95
59.95
59.9
59.9
59.85
59.8
59.85
59.8
59.75
60
59.95
59.9
59.85
59.8
59.75
59.7
59.65
59.75
59.7
59.6
59.55
59.7
59.65
59.65
59.6
59.5
59.6
59.55
59.45
0
2
4
6
8
g
b
c
d
e
f
b
c
d
e
f
g
10
12
14
16
18
b
c
d
e
f
g
Speed_Gen Bus1 #1
20
22
24
26
28
30
26
28
30
Speed_Gen Bus 2 #1
Speed_Gen Bus 3 #1
Figure 4.41: ST1A without - PSS is stable with time 0.3s
65
64
63
62
61
60
59
58
57
56
55
54
53
52
51
50
96
94
92
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
60
58
56
54
52
15
10
5
0
-5
-10
-15
-20
-25
-30
-35
-40
0
2
4
g
b
c
d
e
f
b
c
d
e
f
g
6
8
10
12
14
Rotor A ngle_Gen Bus1 #1
16
b
c
d
e
f
g
18
20
22
24
Rotor A ngle_Gen Bus 2 #1
Rotor A ngle_Gen Bus 3 #1
Figure 4.42: ST1A without - PSS is stable with time 0.3s
50
CHAPTER 5
CONCLUSION
5.1 Conclusion
This work has discussed, the effects of different types of excitation systems, power system
stabilizer (PSS) and automatic voltage regulator (AVR), to ameliorate the transient stability
of generator in power system (phase to ground fault). The design problem for AVR and
PSS is studied to find the performance difference between the models. The studied system
consists of a multi-machine with slack bus system. The types of excitation systems, AVR
IEEE AC1A, ST1A excitation systems, type PSS1A power system stabilizer and type
PSS2A power system stabilizer were chosen. As a result of the study and with reference to
Chapter 4, simulations and results the ST1A model provides greater stability to the power
system was discussed in (Eshraghnia and Kleen, 2014), and the ST1A model under study
more responsive compared to ACA1. The results correspond with (Zhang and Xu, 2007).
The excitation system type AC1A with medium response, while the excitation system type
ST1A with high response. And the results was reported in (Slenduhhov and Kilter, 2013).
From the results obtained, and it was clear that in Case 1 there is harmony between type
ST1A and Type PSS1A power system stabilizer. In Case 2, and with rotor speed the type
ST1A excitation system model without stabilizer It takes about 9 seconds to response to
normal value. Also in Case 3, ST1A has the same performance with PSS2A stabilizer.
There is a little different between Case 1, 2 and 3. But The PSS1A, PSS2A affect
positively in ST1A.
In Case 4, type AC1A excitation system model, there is voltage oscillation output, also
PSS1A is not good choice for type AC1A, this is not best case for AC1A and with more
oscillation in unit 3, but with fast response approximately 4 seconds after the fault
occurrence to return to steady state. The cause of oscillation in unit 3 is the steam turbine
inertia constant (H) at unit 3 and damping coefficient compared to other units.
In Case 5 type AC1A excitation system model without stabilizer the results better than
Case 4. It is medium response, was reported in (Bhaskar et al., 2000).
In Case 6 the system is the best case, and it passed the test time with constant vibration
and show that PSS2A, is suitable with AC1A in this case and have a better damping.
51
Both PSS1A-PSS and PSS2A-PSS are first analyzed. The fault analysis is carried out for
the Chapter 4 test system with both PSS1A-PSS and PSS2A-PSS. And for the rotor angle
during the fault. It is observed that ST1A without PSS and AC1A with PSS2A resulted in
better transient response for single phase faults. This is consistent with previous research,
because the ST1A has fast response, was discussed in (Lubosuy, 2006). For all cases, the
PSS1A affect positively with ST1A, but negatively with AC1A resulted in bad dynamic
response with low frequency oscillations after clearing the fault. But we cannot say that the
PSS1A is not suitable to AC1A, because there are other factors affecting, Xd, Xq, Td0’,
inertia constant (H) and damping coefficient (D).
52
REFERENCES
Grainger, J., & Stevenson, W. Jr. (1994). Power system analysis. New York, NY:
McGraw-Hill.
Anderson, P. M., & Fouad, A. A. (1977). Power system control and stability. Iowa State
University Press, Ames, Iowa.
Kundur, P. (1994). Power system stability and control. New York, NY: McGraw-Hill.
Saadat, H. (1999). Power system analysis. New York, NY: McGraw-Hill.
Padiyar, K. R. (2008). Power system dynamics stability and control. BS Publications.
Wvong, M.D. (1991). Prediction of power system stability by catastrophe theory. In
Proceedings of the IEEE International Symposium on Circuits and Systems (pp. 974-977).
New York, NY: IEEE.
Wang, K., & Crow, M. (2011). Numerical simulation of stochastic differential algebraic
Equations for power system transient stability with random loads. In Proceedings of the
IEEE International Conference on Power and Energy Society General Meeting (pp.1-8).
San Diego, CA: IEEE.
Sumina1,,D., Bulić, N., & Skok,,S. (2011). Stabilization of the electromechanical
oscillations of synchronous generator. Journal for Theory and Application in Mechanical
Engineering, 53 (3), 209-219.
IEEE Standard 421.5. (2006). IEEE Recommended practice for excitation system models
for power system stability studies.
Liu, C., Yokoyama, R., Koyanagi, K., & Lee, K. Y. (2004). PSS design for damping of
inter-area power oscillations by coherency-based equivalent model, Journal of Electrical
Power and Energy Systems, doi:10.1016/j.ijepes.2004.01.007.
53
Lubosuy, Z. (2006). Dual input quasi-optimal PSS for gener-ating unit with static
excitation system, Journal of the Power Plants and the Power Systems Control,
doi:10.3182/20060625-4-CA-2906.00051.
Yeu, R. (2010). Small Signal Analysis Of Power Systems: Eigenvalue Tracking Method
And Eigenvalue Estimation Contingency Screening For Dsa (Doctor’s Thesis, University
Of Illinois At Urbana-Champaign).
Gafari, A., & Muhammed, T. (2013). Critical clearing time evaluation of Nigerian 330kV
transmission system. American Journal of Electrical Power and Energy Systems,
doi: 10.11648/j.epes.20130206.11.
Kawkabani, B., Nicolet, C., & Schwery, A. (2013). Modeling and control of large salientpole synchronous hydro generators and stability issues in isolated production mode. In
Proceedings of the IEEE International Conference Electrical Machines Design Control
and Diagnosis (pp.148 -157). Paris: IEEE.
Taborda, J. (2010). Comparison between detailed and simplified AC exciter models. In
Proceedings of Power and Energy Society General Meeting (pp.1-8). Minneapolis, MN:
IEEE.
Pajuelo, E., Gokaraju, R., & Sachdev, M. S. (2010). Coordination of overexcitation
limiter, field overcurrent protection and generator control. In Proceedings of Power and
Energy Society General Meeting (pp.1-7). Minneapolis, MN: IEEE.
Tang, B. (2011). parameter tuning and experimental results of power system stabilizer
(Master’s Thesis, Louisiana State University).
Martins,,N., & Lima, L. T. G. (1990). Determination of suitable locations for power
system stabilizers and static VAR compensators for damping electromechanical
oscillations in large scale power systems. In Proceedings of Power Industry Computer
Application Conference (pp. 74-82). Seattle, WA, USA: IEEE.
Mummert, C. R. (1999). Excitation system limiter models for use in system stability
studies. In Proceedings of Power Engineering Society Meeting (pp. 187-192). New York,
NY: IEEE.
54
Bose, A. (1984). Application of direct methods to transient stability analysis of power
systems. IEEE Transactions on Power Apparatus and Systems, 7, 1629-1636.
Loen, I. (2014). Stability Analysis of Small Hydro Power Plants (Master’s Thesis,
Norwegian University).
Muriithi, C. M., & Nyakoe, G. N. (2015). Effect of AVR and PSS on power system
transient stability with different wind generation technologies. Journal of Energy
Technologies and Policy, 5, 66-71.
Eshraghnia, R., & Kleen, R. J. (2014). Modeling and simulation of the transient response
of 138.75 MVA synchronous generator with rotating and static excitation systems. In
Proceedings of the T&D Conference and Exposition, 2014 IEEE PES (pp. 1-5). Chicago,
IL, USA: IEEE.
Lee, S., Kang, S., Jang, G., Li, S., Park, J., Moon, S., & Yoon, Y. (2006). Damping
analysis using PSS1A PSS & PSS2A PSS for power system in South Korea. Journal of
Electrical Engineering & Technology, 1, 271-278.
Zhang, F., & Xu,, Z. (2007). Effect of exciter and PSS on SSR damping. In Proceedings
of Power Engineering Society General Meeting (pp. 1-7). Tampa, FL: IEEE.
Slenduhhov, V., & Kilter, J. (2013). Modeling and analysis of the synchronous
generators
excitation
systems,
Parnu.
Retrieved
Jul
12,
2013,
from
http://egdk.ttu.ee/files/parnu2013/Parnu_2013_252-257.pdf
Bhaskar, R., Crow, M. L., Ludwig, E., Kelvin, T. E., & Shah, K. S. (2000). Nonlinear
parameter estimation of excitation systems. IEEE Transactions On Power Systems, 15,
1225 - 1231.
Ferguson, R.W., Herbst, R., & Miller, R.W. (1959). Analytical studies of the brushless
excitation system. AIEE Transactions on Power Apparatus and Systems, 79, 1815-1821.
Gayek, H. (1964). Transfer characteristics of brushless aircraft generator systems. IEEE
Transactions on Aerospace, 2, 913-928.
55
Nallagalva, S., Kirar, M., & Agnihotri, G. (2012). Transient stability analysis of the IEEE
9-Bus electric power system. International Journal of Scientific Engineering and
Technology , 1, 161-166.
Coelho, M. (2013). Optimal Location of FACTS to Optimize Power System Security.
(Master’s Thesis, tecnico lisboa).
Wang, Xi-Fan., Song, Y., & Irving, M. (2008). Modern power systems analysis. New
York, NY: Springer Science & Business Media.
Agatep,,,A.,,(2013).
Voltage
Stability
Analysis
Using
Simulated
Synchrophasor
Measurements. (Master’s Thesis, California Polytechnic State University).
Ying, N.Z., & Jian, X. J. (2013). Simulation analysis of a synchronous generator system
under fault conditions. In Proceedings of the International Conference on Applied
Superconductivity and Electromagnetic Devices (pp.180-184). Beijing: IEEE.
56
APPENDIX A
Reduced And Generator Data
Table A.1: Generator data
Table A.2: Reduced Y matrices
57
APPENDIX B
Excitation System, AVR And PSS Models
Figure B.1: AC1A Excitation system model
Table B.1: AC1A Data
58
Figure B.2: ST1A Excitation system model
Table B.2 ST1A data
Figure B.3: PSS1A model
59
Table B.3: PSS1A data
Table B.4: PSS1A data
Figure B.4: PSS2A model
60
Table B.5: PSS2A data
Figure B.5: IEEEG1 Governor
61
APPENDIX C
Before Fault And Fault Analysis
Table C.1: Before fault-generators
Name
of
Max Min
Max Min
Bus
Mvar Mvar
MW MW
Bus1 9900
-9900 1000
0
Bus 2 9900
-9900 1000
0
Bus 3 9900
-9900 1000
0
AVR
YES
YES
YES
AGC
YES
YES
YES
Set
Gen
Gen
Volt Mvar
MW
1.04
27.04 71.64
1.025
6.65
163
1.025
-10.86
85
Status
Closed
Closed
Closed
Table C.2: Before fault-bus data
Gen
Gen
Load Load
Mvar
MW
Mvar MW
27.04 71.64
6.65
163
-10.86
85
50
30
35
Angle Volt
Nom
(Deg) (kV)
PU Volt kV
0
17.16
1.04 16.5
9.28
18.45
1.025
18
4.67
14.145
1.025 13.8
-2.22 235.932 1.02579
230
125
-3.99 228.997 0.99564
230
90
-3.69 232.912 1.01266
230
3.72 235.928 1.02577
230
100
0.73 233.654 1.01589
230
1.97 237.442 1.03236
230
Name
Bus1
Bus 2
Bus 3
Bus 4
Bus 5
Bus 6
Bus 7
Bus 8
Bus 9
Table C.3: Before fault-lines and transformers
To
Name
Bus1
Bus 7
Bus 3
Bus 4
Bus 4
Bus 5
Bus 6
Bus 8
Bus 9
From Mvar MW MVA
Mvar
MW
Name Loss
Loss From
From
From
Bus 4
3.12
0
75.5
-23.9 -71.6
Bus 2 15.83
0
163.1
6.6
163
Bus 9
4.1
0
86.3
15
-85
Bus 5 -15.79 0.26
56.1
-38.7 -40.7
Bus 6 -15.51 0.17
34.7
-16.5 -30.5
Bus 7 -19.69
2.3
87
-8.4
86.6
Bus 9 -31.53 1.35
63.4
-18.1
60.8
Bus 7
-11.5 0.48
76.4
-0.8
76.4
Bus 8 -21.18 0.09
34.2
-24.3 -24.1
62
Device
Type
Transformer
Transformer
Transformer
Line
Line
Line
Line
Line
Line
Table C.4: Before fault-loads
Name
of Bus
Bus 5
Bus 6
Bus 8
Number
of Bus
Mvar
MVA
Mvar MW
Status
5
50 134.63
50
125 Closed
6
30
94.87
30
90 Closed
8
35 105.95
35
100 Closed
Table C.5: Fault analysis
Table C.6: Fault-generators
Phase
Phase
Ang
Phase
Ang
Phase
Phase
C
Ang B
A
Cur C
Cur B
118.43 -168.94 -27.73
1.1365 1.01021
133.78 -132.78
-6.75 2.10693 1.65581
137.77 -141.86 -12.13 1.31805 0.85957
63
Phase
Cur A
1.73142
2.60041
1.68972
Name
of
Bus
Bus
Bus1
1
Bus 2
2
Bus 3
3
Table C.7: Fault-bus
Phase
Phase
Phase
Phase
Phase
Phase
Ang C
Ang B
Ang A Volt C
Volt B
Volt A
100.59
-117.3 -59.63
1.34542
0.53886
0.97787
107.16 -103.94 -58.48
1.35498
0.47136
0.98204
104.2 -108.91 -56.68
1.29979
0.53847
0.89828
103.81
123.74
97.7
3.06028
1.43878
0.69244
102.81
124.06 104.61
2.93292
1.37556
0.42963
102.95
122.12
100.7
3.1246
1.52882
0.81656
106.08
124.15
90.71
2.90212
1.22711
0.40424
104.69
122.85
98.07
3.0028
1.36309
0.61741
105.29
121.91
95.61
3.11971
1.43991
0.84868
105.06
127.15
18.61
2.79
1.16903
0.00679
Name
Bus1
Bus 2
Bus 3
Bus 4
Bus 5
Bus 6
Bus 7
Bus 8
Bus 9
FaultPt
Table C.8: Fault-line
Phase
Cur C
To
1.1365
2.10693
1.31805
0.68321
0.5729
0
1.02252
0.82133
0.8732
0.99569
0.41027
Phase
Cur B
To
1.01021
1.65581
0.85957
0.47841
0.54996
0
0.48437
0.22426
0.60317
0.67801
0.19457
Phase
Cur A
To
1.73142
2.60041
1.68972
2.11075
0.86622
0
2.62969
0.6135
1.7913
4.25658
1.40497
Phase
Cur C
From
1.1365
2.10693
1.31805
0.91813
0.43234
0
0.99578
0.96478
0.97741
1.13037
0.71609
Phase
Cur B
From
1.01021
1.65581
0.85957
0.30774
0.32405
0
0.6781
0.69808
0.79087
0.86598
0.14067
Phase
Cur A
From
1.73142
2.60041
1.68972
2.20629
0.77769
0
2.64344
0.4118
1.85687
4.17474
1.55689
To
Name
Bus1
Bus 7
Bus 3
Bus 4
Bus 4
Bus 5
Bus 5
Bus 6
Bus 8
FaultPt
Bus 9
Table C.9: Fault-loads
Phase
Phase
Phase
Cur C
Cur B
Cur A
1.89492
0.57346
1.53425
1.23868
0.45546
0.92229
1.40722
0.47159
1.06882
64
Name of
Bus
Bus 5
Bus 6
Bus 8
From
Name
Bus 4
Bus 2
Bus 9
Bus 5
Bus 6
Bus 7
FaultPt
Bus 9
Bus 7
Bus 7
Bus 8
APPENDIX D
Transient Analysis
Table D.1: AC1A with PSS1A
Time
Max
Speed
4.975
4.433
4.391
Max
Speed
Time
Min
Min
Speed Speed
Time
Max
Max
Angle Angle
Time
Min
Min
Angle Angle
60.351
60.418
60.246
4.341
4.108
4.108
5.208
4.683
4.625
4.675
5.233
5.125
59.787
59.72
59.76
11.869
89.349
61.326
-31.774
56.173
49.478
Name
Original of
Angle
Bus
3.586 Bus1
61.1 Bus 2
54.138 Bus 3
Table D.2: AC1A with PSS1A
Name
MaxTime
Time
of
Original Min
Max
Max
Min
Min
Original
Bus
Efd
PMech PMech PMech PMech PMech PMech
Bus1
1.0821 18.939
4.508 78.576
5.141 59.637
71.645
Bus 2
1.7893 13.208
0
163
4.616 149.792
163
Bus 3
1.403 10.789
4.233 89.062
4.608 78.273
85
Table D.3: AC1A with PSS1A
Name Maxof
Min Max Min
Bus
Vs
Vs
Vs
Bus1
0.2
0.1 -0.1
Bus 2
0.2
0.1 -0.1
Bus 3
0.2
0.1 -0.1
Max
Ifd
1.2161
2.4521
1.8824
Min
Original Max
Min
Ifd
Ifd
Efd
Efd
1.0821
1.0821 3.7211
0
1.367
1.7893 4.3209 -0.9624
1.2125
1.403 3.5302
0
Table D.4: AC1A with PSS1A
Time
Time
Time
Time
Max Max
Min
Min
Max Max
Min
Min
Original
Hz
Hz
Hz
Hz
Volt Volt
Volt Volt
Volt
Name
5 60.2888 4.35 59.8455 5.15 1.1086
4.6 0.9578
1.04 Bus1
4.5
4.5
4.966
4.966
5.216
4.5
4.516
4.516
60.3886
60.225
60.2404
60.2404
60.1523
60.3466
60.2932
60.2134
4.108
4.108
4.108
4.108
4.108
4.108
4.108
4.108
59.7586
59.7972
59.8794
59.851
59.8527
59.7836
59.7919
59.8048
4.108
5.366
5.183
5.183
5.233
4.108
5.366
5.35
1.0968
1.0857
1.0742
1.0201
1.057
1.0867
1.0695
1.0865
65
4.666
4.683
4.65
4.65
4.666
4.683
4.683
4.683
0.9135
0.8563
0.8743
0.8303
0.7986
0.8761
0.8356
0.8351
1.025
1.025
1.0258
0.9956
1.0127
1.0258
1.0159
1.0324
Bus 2
Bus 3
Bus 4
Bus 5
Bus 6
Bus 7
Bus 8
Bus 9
Table D.5: AC1A with PSS2A
Time
Time
Time
Time
Max
Max
Min
Min
Max
Max
Min
Min
Original Name
Speed Speed Speed Speed Angle Angle Angle Angle
Angle
of Bus
4.958
60.3 4.333 59.791 5.208
11.55
4.65 -27.156
3.586 Bus1
4.425 60.37 4.108
59.72 4.691 87.034 5.225
57.953
61.1 Bus 2
5.358 60.23 4.108 59.761 4.541 60.544 5.141
48.923
54.138 Bus 3
Table D.6: AC1A with PSS2A
MaxTime
Time
MaxMin
Max
Max
Min
Min
Original
Min
PMech PMech PMech
PMech
PMech
PMech
Speed
17.11
4.5
78.411
5.141
61.301
71.645
0.5084
11.534
0
163
4.6 151.466
163
0.6498
11.719
4.233
89.049
5.558
77.33
85
0.4694
Table D.7: AC1A with PSS2A
Max
Vs
0.1
0.1
0.075
Min
Original Max
Min
Original Max
Min
Original
Vs
Vs
Ifd
Ifd
Ifd
Efd
Efd
Efd
-0.1
0
1.172 1.076
1.0821 3.2403
0
1.0821
-0.0667
0 2.3245 1.386
1.7893 3.567 -0.0609
1.7893
-0.0216
0 1.8803 1.2529
1.403 3.7558
0.1794
1.403
Table D.8: AC1A with PSS2A
Time
Max Max
Hz
Hz
4.983 60.2481
4.466 60.3373
5.408 60.2134
4.975 60.2087
4.975 60.2087
5.275 60.1408
4.466 60.3004
4.466 60.2543
5.408
60.21
Time
Min
Hz
4.35
4.108
4.108
4.108
4.108
4.108
4.108
4.108
4.108
Min
Hz
59.8495
59.7588
59.7973
59.8794
59.8511
59.8528
59.7837
59.792
59.8048
Time
Max Max
Volt Volt
5.058
1.062
4.108 1.0966
5.291 1.0737
5.1 1.0325
0 0.9956
5.175 1.0267
4.108 1.0864
4.108 1.0648
5.275 1.0741
66
Time
Min
Min
Original
Volt Volt
Volt
Name
4.583 0.9579
1.04 Bus1
4.683 0.9275
1.025 Bus 2
4.666 0.8965
1.025 Bus 3
4.616 0.8871
1.0258 Bus 4
4.616 0.8424
0.9956 Bus 5
4.65 0.8298
1.0127 Bus 6
4.683 0.8997
1.0258 Bus 7
4.666 0.8683
1.0159 Bus 8
4.666 0.8756
1.0324 Bus 9
Table D.9: AC1A without PSS
Time
Max
Max
Speed Speed
Time
Min
Min
Speed Speed
Time
Max Max
Angle Angle
Time
Min
Min
Angle Angle
4.991
5.45
5.366
4.35
5.008
4.108
5.233 18.442
4.691 91.172
4.533 59.781
4.683
5.25
7.05
60.334
60.544
60.28
59.781
59.602
59.76
-31.37
50.71
48.774
Original Name
Angle
of Bus
3.586 Bus1
61.1 Bus 2
54.138 Bus 3
Table D.10: AC1A without PSS
Time
Time
Max-Min Max
Max
Min
Min
Original
PMech
PMech
PMech
PMech
PMech
PMech
18.438
4.516
78.85
5.158
60.412
71.645
16.752
0
163
5.616
146.248
163
13.6
5.166
90.145
5.608
76.545
85
Table D.11: AC1A without PSS
Max Min Original Max
Min
Original Max
Min
Original
Vs
Vs
Vs
Ifd
Ifd
Ifd
Efd
Efd
Efd
0
0
0 1.2326 1.0821
1.0821 2.5811
0.2163
1.0821
0
0
0 2.4774 1.3588
1.7893 4.9545 -0.0455
1.7893
0
0
0 1.8702 1.2465
1.403 3.8404
0.1219
1.403
Table D.12: AC1A without PSS
Time
Max Max
Hz
Hz
5 60.2686
5.483 60.4084
5.45 60.2338
4.958 60.2239
4.958 60.2239
4.883 60.1478
5.483 60.3621
5.483 60.3063
5.466 60.2284
Time
Min
Hz
4.366
5.041
4.108
4.266
4.108
4.108
5.05
4.108
4.108
Min
Hz
59.839
59.6991
59.7971
59.8792
59.851
59.8527
59.7453
59.7918
59.8047
Time
Max
Max
Volt
Volt
5.083 1.0884
4.108 1.0969
5.158 1.0803
5.116 1.0603
5.116 1.0069
5.15 1.0532
5.15
1.091
5.15 1.0754
5.15 1.0864
67
Time
Min
Volt
4.6
4.65
4.683
4.65
4.65
4.683
4.666
4.683
4.683
Min
Original
Volt
Volt
Name
0.9868
1.04 Bus1
0.8979
1.025 Bus 2
0.8633
1.025 Bus 3
0.9004
1.0258 Bus 4
0.855
0.9956 Bus 5
0.8186
1.0127 Bus 6
0.8652
1.0258 Bus 7
0.8308
1.0159 Bus 8
0.8407
1.0324 Bus 9
Table D.13: ST1A with PSS1A
Time
Max
Speed
5.008
5.408
5.341
Time
Time
Time
Max
Min
Min
Max Max
Min
Min
Original Name
Speed Speed Speed Angle Angle Angle Angle
Angle
of Bus
60.257
4.35 59.785 4.167
8.356
4.666 -24.719
3.586 Bus1
60.345 4.108 59.715 4.683 85.127
4.167
57.869
61.1 Bus 2
60.235 4.108 59.763 4.533 59.003
6.041
49.942
54.138 Bus 3
Table D.14: ST1A with PSS1A
Name of
Bus
Bus1
Bus 2
Bus 3
Time
Time
Max
Max
Min
Min
Original
PMech
PMech
PMech
PMech
PMech
4.516
78.752
5.208
62.501
71.645
0
163
5.583
151.597
163
4.233
89.066
5.575
76.674
85
Table D.15: ST1A with PSS1A
Name
of
Max
Min
Original MaxI
Bus
Vs
Vs
Vs
fd
Bus1 0.0853
-0.1
0 1.1692
Bus 2
0.1
-0.1
0 2.2706
Bus 3
0.1
-0.1
0 1.7722
Min
Original Max
Ifd
Ifd
Efd
1.0821
1.0821 1.6265
1.4267
1.7893 2.5481
1.2644
1.403 2.2939
Min
Original
Efd
Efd
0.6565
1.0821
1.2624
1.7893
0.8874
1.403
Table D.16: ST1A with PSS1A
Time
Max Max
Hz
Hz
5.066 60.2204
Time
Time
Time
Min
Min
Max Max
Min Min
Original
Hz
Hz
Volt Volt
Volt Volt
Volt
Name
4.366 59.8397 6.833
1.072 4.633 0.9777
1.04 Bus1
5.433
5.416
5.108
5.108
5.333
5.433
5.433
5.416
4.108
4.108
4.316
4.108
4.108
4.108
4.108
4.108
60.3066
60.2397
60.1957
60.1957
60.1895
60.2892
60.2683
60.2388
59.7681
59.803
59.8811
59.8555
59.857
59.7916
59.7992
59.8107
4.108
6.916
6.116
0
6.125
4.108
4.108
6.916
1.1026
1.0772
1.0399
0.9956
1.0295
1.0917
1.0692
1.0739
68
4.733
4.716
4.666
4.666
4.683
4.716
4.7
4.7
0.9298
0.9019
0.9076
0.8619
0.8514
0.9057
0.8772
0.8867
1.025
1.025
1.0258
0.9956
1.0127
1.0258
1.0159
1.0324
Bus 2
Bus 3
Bus 4
Bus 5
Bus 6
Bus 7
Bus 8
Bus 9
Table D.17: ST1A with PSS2A
Time
Max Max
Hz
Hz
5.075 60.2255
5.466 60.3292
5.45 60.2664
5.125 60.2017
5.125 60.2017
5.4 60.2084
5.466 60.3126
5.458 60.2925
5.45 60.2642
Time
Min
Min
Hz
Hz
4.366 59.8412
4.108 59.7682
4.108 59.8032
4.3 59.8818
4.108 59.8556
4.108 59.8571
4.108 59.7917
4.108 59.7993
4.108 59.8109
Time
Max Max
Volt Volt
6.866 1.0515
4.108 1.1025
6.983 1.0732
0 1.0258
0 0.9956
6.95
1.017
4.108 1.0916
4.108
1.069
4.108 1.0701
Time
Min
Volt
4.633
4.733
4.716
4.666
4.666
4.683
4.716
4.716
4.7
Min
Original
Volt
Volt
Name
0.9802
1.04 Bus1
0.9255
1.025 Bus 2
0.8986
1.025 Bus 3
0.9094
1.0258 Bus 4
0.8636
0.9956 Bus 5
0.8518
1.0127 Bus 6
0.9016
1.0258 Bus 7
0.8735
1.0159 Bus 8
0.884
1.0324 Bus 9
Table D.18: ST1A with PSS2A
Time
Max
Speed
5.025
5.433
5.383
Time
Time
Time
Max
Min
Min
Max
Max
Min
Min
Original Name
Speed Speed Speed Angle Angle Angle Angle
Angle
of Bus
60.261
4.35 59.787
4.167
8.358
4.675 -24.876
3.586 Bus1
60.367 4.108 59.715
4.691 85.218
4.167 57.866
61.1 Bus 2
60.267 4.108 59.763
4.533 59.446
6.941 49.899
54.138 Bus 3
Table D.19: ST1A with PSS2A
Name of
Bus
Bus1
Bus 2
Bus 3
MaxTime
Time
Min
Max
Max
Min
Min
Original
PMech
PMech
PMech
PMech PMech
PMech
16.438
4.516
78.698
5.225
62.26
71.645
12.439
0
163
5.608 150.561
163
13.526
4.233
89.073
5.591
75.547
85
Table D.20: ST1A with PSS2A
Max
Min
Original
Original
Vs
Vs
Vs
MaxIfd MinIfd Ifd
0.1
-0.1
0 1.1632 1.0821
1.0821
0.1 -0.0638
0 2.2654 1.4324
1.7893
0.0741 -0.0127
0 1.7683 1.2724
1.403
69
Max
Efd
1.6444
2.4768
2.1219
Min
Original
Efd
Efd
0.6271
1.0821
1.2897
1.7893
0.9252
1.403
Table D.21: ST1A without PSS
Time
Max Max
Hz
Hz
5.091
60.244
5.483 60.3467
5.466 60.2747
5.133 60.2186
5.133 60.2186
5.391 60.2152
5.483 60.3278
5.483 60.3049
5.466 60.2728
Time
Min
Min
Hz
Hz
4.383 59.8349
4.108 59.7678
4.108 59.8028
4.333 59.8765
4.108 59.8554
4.108 59.8569
4.108 59.7914
4.108
59.799
4.108 59.8106
Time
Time
Max Max
Min
Volt Volt
Volt
6.983 1.0645 4.666
4.108 1.1028 4.733
7.066 1.0721 4.733
7.016 1.0341 4.683
0 0.9956 4.683
7.016 1.0248
4.7
4.108
1.092 4.733
4.108 1.0695 4.716
4.108 1.0708 4.716
Min
Original
Volt
Volt
Name
0.9813
1.04 Bus1
0.9093
1.025 Bus 2
0.8832
1.025 Bus 3
0.9056
1.0258 Bus 4
0.86
0.9956 Bus 5
0.8412
1.0127 Bus 6
0.8843
1.0258 Bus 7
0.856
1.0159 Bus 8
0.8675
1.0324 Bus 9
Table D.22: ST1A without PSS
Time
Max
Speed
5.041
5.45
5.383
Time
Time
Time
Max
Min
Min
Max
Max
Min
Min
Original
Speed Speed Speed Angle Angle Angle Angle
Angle
60.281
4.35
59.78
4.167
8.36
4.683 -26.583
3.586
60.391 4.108 59.715
4.691 86.823
4.167
57.873
61.1
60.279 4.108 59.762
4.533 59.294 11.608
50.206
54.138
Name
of Bus
Bus1
Bus 2
Bus 3
Table D.23: ST1A without PSS
Time Max
Max
Time Min Min
Original
PMech
PMech
PMech
PMech
PMech
4.525
78.942
5.241
61.506
71.645
0
163
5.633
149.729
163
4.233
89.088
5.608
75.042
85
Table D.24: ST1A without PSS
Max Min
Vs
Vs
0
0
0
Original
Vs
0
0
0
0
0
0
Max
Ifd
Min
Ifd
Original Max
Ifd
Efd
1.1746 1.0821
2.287 1.4257
1.7766 1.2667
70
1.0821
1.7893
1.403
Min
Efd
1.4333 0.9276
2.2892 1.3284
2.0499 1.001
Original
Efd
1.0821
1.7893
1.403
APPENDIX E
Differential-Algebraic Equations Method
Figure E.1 Differential- algebraic Equations method applied to transient stability
71